The science of alchymy I like very well, and indeed, 'tis the philosophy of the ancients. I like it not only for the profits it brings in melting metals, in decocting, preparing, extracting and distilling herbs, roots; I like it also for the sake of the allegory and secret signification, which is exceedingly fine, touching the resurrection of the dead at the last day.
Martin Luther's Table Talk 
Traditional alchemy was a protoscience that combined chemistry, physics, metallurgy, medicine, astrology, mysticism, and religion. At a fundamental practical level, alchemy was pure research, involving the combination of different materials and chemicals and studying the results. In this sense it was one of the first true sciences, for the fact that alchemists preferred to test their theories and hypotheses for themselves, rather than take the word of an authority such as the Church.
There are several theories as to the origin of the word 'alchemy':
Most alchemists were seeking the philosopher's stone, with the generally accepted theory that a final substance (or 'stone') would be created out of a series of chemical reactions, and the final result would be a substance powerful enough to transmute one substance into another. Commonly the intention was to change lead — the most base metal — into gold, which was considered the ultimate metal. Not incidentally, most patrons were also interested in an easy creation of gold, and thus bankrolled their personal alchemists in hopes that they would be the first to have access to the alchemist's final success.
Of course, success never happened, but alchemists discovered a number of early chemical facts along the way. And a few probably blew up their labs in the meantime, but alchemy generally consisted of actions such as 'mix two pounds of saltpeter with one pound of sulfur, then boil until something happens.' Whether the resulting substance was inert, poisonous, or explosive, the alchemist noted this and continued with a different set of metals or chemicals.
The alchemical operation consisted essentially in separating the prima materia, the so-called chaos, into the active principle, the soul, and the passive principle, the body, which were then reunited in personified form in the coniunctio or 'chymical marriage'... the ritual cohabitation of Sol and Luna.
C.G. Jung, Mysterium Coniunctionis 
Today, alchemy is considered a pseudoscience, in that it operates based on a faulty assumption; that is, that a chemically-produced substance could alter another substance on the molecular level. However, alchemy was often treated as a metaphor, or process, that could be applied to all aspects of life, and not just in a chemical sense. These days, alchemy is often considered a mystical or philosophical branch of study, where the substance in the crucible is not sulfur and mercury, but the person's experiences and psyche.
In chapter 10 of the manga, Edward is reviewing research documents, and explains to a non-alchemist, "To an ordinary person, it looks like...culinary research documents... But they really are highly advanced files on alchemy with many hidden meanings and metaphors that only the one who wrote would understand."
Most of the early alchemists' texts are encoded for the same reasons. For the most part, no one wanted their notes to be decipherable if they fell into the wrong hands. In this case, 'the wrong hands' could be both alchemical competitors, or the Church. And it could also be the alchemist's patron, who might wish to determine for himself (or herself) just what the alchemist was up to.
Many of the alchemical texts that survive are couched in poetry and pictures, with a heavy use of metaphor, both religious and mythological. From a more cynical point of view, alchemical studies were utter failures when it came to achieving the philosopher's stone, but that was the last thing an alchemist wanted anyone to discover.
Conclusion: FMA is an accurate representation of historical alchemical record-keeping practices.
In chapters 1-13 of the manga, and 16 episodes of the anime, not once has Edward (or any other alchemist) transformed one object into a different object not made of the same chemical or molecular properties as the first. Even when Edward 'creates' gold, he does so not by creating gold, but by reshaping coal into ingots and covering it with gold. By the end of the episode, the false gold is revealed as such. Alphone explains that he cannot create a larger radio with the parts of a smaller radio, and even the walking statues in Liore (or Riore) are made from the stone of the destroyed building.
Traditional alchemy, in contrast, was not concerned with the Laws of Conservation, which were a discovery off in the future, at that time. Most of the alchemical discoveries were, in fact, re-discoveries of scientific facts lost during the Dark Ages. Alchemists were not concerned with whether they observed a law of equivalent trade; the notion didn't even really exist at the time.
Conclusion: The emphasis on a Law of Conservation fits the scientific mindset that pervaded alchemy, even if it uses a concept that's common now more than then. This underlines the mangaka's interpretation of Alchemy as a 'science', even if it's not entirely accurate to the traditional.
In several of the anime episodes, the Philosopher's Stone is referred to as an entity with a variety of names, fitting the fact that it has a variety of possible appearances: liquid when bottled, solid when exposed to the air. There are a number of chemicals that have odd properties, which fascinated alchemists. Mercury was a favorite, for its solid yet liquid tendencies, for instance. The Philosopher's Stone was often gived coded names, as well, both to protect the writer's research and to protect the alchemist from threats from the Church.
However, the original Alchemists did not use human souls, dead bodies, pregnant women, or small furry animals to create the stone. They were interested in chemicals, and exploring the chemical properties of substances. There are alchemical texts that speak of adding hair, fingernail clippings, fur, feathers, bones, and other such items, usually on the theory that such substances might have their own chemical properties that would add something to the reaction. In some ways, they might: fingernails retain potassium, and potash is a major ingredient in lye, a corrosive chemical.
But when alchemy is taken from its mystical, philosophical point of view, then the addition of a human soul becomes the major basis of the equation. When the alchemists began to apply this "throw it into the crucible, burn off the bad, and find the pure results" to his own psyche, then yes, one could say that a human soul became part of the philosopher's stone, if the stone is a metaphor for that which transforms a base, material-oriented person into an enlightened being.
Conclusion: if FMA takes the route that 'human souls' or 'deaths' is a metaphor for the final product (and not an actual ingredient), then it's closer to alchemy as a philosophical course of study. But there's nothing wrong with artistic license, and it does make for a better story if there's the risk that someone might die.
One theme running through FMA — and no coincidence, probably, that it was introduced in both the first chapter of the manga as well as the first episode of the anime — is the issue of alchemy/science versus faith/religion. Because the original alchemists were operating at a time when the Western/European world was slowly crawling out from the shadow of the Dark Ages, they had to contend with an extremely strong Church that wanted its subjects to, well, remain subject. Alchemists threatened that strength, by preferring to discover for themselves, rather than sit back and wait for a diety to grant them the knowledge or ability.
Most of the early scientific practices rooted in alchemy are based on the belief that one must taste, touch, see, feel, hear and smell a tangible result — and be able to duplicate it — rather than take the results for granted. As the Church's tendency was to tell the unwashed masses to 'trust in God,' the alchemists who preferred to find out for themselves were practicing and preaching a dangerous concept.
Much of the mystical, hermetic, and gnostic traditions interwoven with philosophical-type alchemy stem from this insistence that one experience the results for oneself. Gnosticism, with its insistence on self-knowledge of the divine, dovetails in some ways with alchemical thought processes.
A mystic and an alchemist are partially overlapping sets, neither mutually exclusive nor inclusive. A mystic seeks connection to the transcendent (a diety, usually) and may or may not seek self-transformation. An alchemist's priority is self-transformation, and may or may not use a connection to the transcendent as the means to do so. It's a sweeping generalization in both cases, but enough to explain the similiarities and differences.
Conclusion: FMA is using the historical tension between the medieval Christian Church and alchemists, and echoing the same questions raised then.
Van (or Von) Hohenheim, Edward and Alphone's father, gets his name from a town in Germany. It's also the surname of Philippus Aureolus Theophrastus Bombastus von Hohenheim, more often referred to as Theophrastus von Hohenheim, an alchemist with the penname of Paracelsus. Von Hohenheim, on its own, is the equivalent of calling oneself something like Jack of London. However, it indicates Arakawa spent at least some time digging through introductory alchemical histories or texts, that he would chose such a name for the boys' father.
"Paracelsus was a medical reformer who introduced a new concept of disease and the use of chemical medicines. He studied at several Italian universities and began to practice medicine and surgery in the 1520s. A difficult personality, he created controversy because of his wholesale condemnation of traditional science and medicine. He never obtained a secure academic position or permanent employment.
Paracelsus's new concept of disease emphasized its causes to be external agents that attack the body, contrary to the traditional idea of disease as an internal upset of the balance of the body's humors (yellow bile, black bile, blood and phlegm). Therapy, according to Paracelsus, was to be directed against these agents of disease, and for this he advocated the use of chemicals rather than herbs. Alchemy became the means of preparing such chemicals; in this way Paracelsus changed the emphasis of the alchemical art from chasing the elusive Elixir of Life or Philosopher's Stone, to making medicines." 
Listed in order of introduction in (first) anime. 
There are two predominant historical perspectives on what homonculi (sing: homonculus) are.
Creation of a homunculus requires semen and blood, which are considered carriers of the "pneumamaterial prima, or elemental matter of which, in alchemical theory, all substances were ultimately composed." 
According to Paracelsus,
A man's semen must be put into a hermetically — sealed retort, buried in horse manure for 40 days, and magnetized'. During this time, it begins to live and move, and at the end of the 40 days it resembles a human form, but is transparent and without a body. It must now be fed daily with the arcanum (hidden mystery) of human blood (arcanum sanguinis hominis), and be maintained at the constant temperature of a mare's womb, for a period of 40 weeks, and it will grow into a human child, with all its limbs developed, as normal as any child born of a woman, except that it will be much smaller. It may be raised and educated like any other child, until he grows older and obtains reason and intellect, and is able to take care of himself.
A homunculus, traditionally, is almost like Tom Thumb — a 'small man' or 'little man', which mystically reflects the 'great man' of the macrocosm (universe). The homunculus, then, is the microcosm. Many of the mystical elements around alchemy were influenced by Qabbalism, Hermeticism, and Gnosticism, which have a common sub-theme of 'as above, so below.' One way to interpret this adage is to see humanity's creations as 'smaller' versions of creations by the divine.
Homunculi are believed to have difficulty existing in their bodies, which shows up as awkward or stilted movement. Some alchemists expected homunculi, due to their non-natural origins, to have characteristics similar to what we would now consider robotic. Homunculi were not always expected to have higher reasoning, such as language or arts, but some alchemists argued that as a miniature person, the homunculus could be taught.
In comparison, the golem — a one-time creation of legend — did not have any higher reasoning, but was a weapon created solely for protecting the Jewish residents of the city against a pogram. When the golem achieved its purpose, according to some versions, it crumbled back into the dust from which it was created.
"To raise such life-forms one must fully understand the Power of Self and the Powers which surround. Faith, the Will, and the imagination may accomplish much. When one has attained such levels, one may use any form of ceremony to bring life into inanimate (statuette) objects. But this is temporary, as the life-force becomes deprived of its energy (arcanum sanguinis hominis / spermae), then it begins to wither and requires sustenance." 
Some homunculi are created fully formed, such as the type Paracelsus described. Others are dolls instilled with a spirit of some type, or through the use of the elemental matter of sperm or blood. In today's world, test tube babies are the closest to homunculi, being essentially the same process as described, requiring two items (semen and egg) that form the basis of life.
From an entry by Northblue, on the FMA LiveJournal Communities:
Ed's alchemical symbol is actually a little unusual. See, in real alchemy, they almost always use a PAIR of serpents. The two serpents represent sulphur (the male principle) and mercury (the female principle). The alchemists thought that since creation happens through reproduction, true transmutation could only be accomplished through the unification of the male and female elements. The other symbol commonly employed by the alchemists was the phoenix. Since transmutation destroyed one thing to make another, they likened it to the phoenix's rebirth (with the unification of sulphur and mercury counting as "conception").
Sometimes they used lions instead of serpents. And sometimes salt is in there too, as a neutral element. But that's besides the point.
A single serpent is usually only seen when it's eating its own tail. Then it's Oroborus — the circle of eternity. But in Ed's symbol there's no tail-eating to speak of. Although the wings beside the crown may be representative of the transmutation phoenix. It's often depicted in similar ways in real life alchemical literature.
Either the author decided to use the symbol because it was Biblical, or he just didn't do a lot of research on alchemy! Although I'm rather impressed that they included Red Tincture in the series, which real alchemists also thought was equivalent to the Philosopher's Stone.
An addendum to the phoenix thing: The phoenix also represented the Philosopher's Stone. That's why the Philosopher's Stone and the Red Tincture were theorized to be, well, red. Red was the color of the phoenix. Many theorists thought that the Philosopher's Stone could be created by a four step process, which they represented with birds. It went from crow, to swan, to peacock, to the phoenix finished product. Diagrams of this process almost always show the "monarch" phoenix at the top.
A chimera is a hybrid. In Greek mythology, the original Chimera (or Chimeara) was a female fire-breathing monster with a lion's head, a goat's body, and a serpent's tail.
Medicine pre-empted the term, applying it as a 'hybrid,' when it was first discovered that some people had two different blood types. A chimera is "a person composed of two genetically distinct types of cells. Most [people with two blood types] proved to be 'blood chimeras' — non-identical twins who shared a blood supply in the uterus. Those who were not twins are thought to have blood cells from a twin that died early in gestation. Twin embryos often share a blood supply in the placenta, allowing blood stem cells to pass from one and settle in the bone marrow of the other. About 8% of non-identical twin pairs are chimeras." 
Chimera is also an archaic term for hermaphrodite, in which one person carries the reproductive organs for both genders. While it's rare for both sets of reproductive organs to develop, it's virtually unheard of for both sets to be fully operational. The application of 'chimera' as a concept of hybridism still applies, however.
All images from Toriyama's World.
Many of the military names in FMA are related to WWII fighter planes, and the relationship between the characters and the aircraft's capabilities are sometimes intriguing. Note: the discussion of ranks are per the first anime series (Fullmetal) and not the mangaverse/Brotherhood canon.
Bradley Fighting Vehicle M-2/M-3 is a light-armored, midrange tank designed for mechanized infantry and armored cavalry combat. Main armament is a 25mm cannon, with supplementary armament of a TOW missile and a 7.62mm machine gun. The Bradley is a modern tank. 
Bradley may have a WWII connection as well. Omar Bradley was originally teacher at U. S. Military Academy and the Infantry School, but he rose quickly through the ranks due to his brilliant tactician skills and his reputation as a commander with whom his soldiers could readily identify. By 1945, Bradley was in charge of the 12 U.S. Army Group in the European arena, commanding roughly 1,300,000 men.
"His troops broke out of the Normandy beachhead, liberated Paris, defeated a German counteroffensive during the winter of 1944-1945, seized the first bridgehead over the Rhine River, and drove through central Germany to establish the first Allied contact with troops of the Soviet Union." 
After WWII, Bradley took administrative positions, becoming the US Army's Chief of Staff in 1948. He was the fourth officer ever to reach the rank of 5-star general in the Army, a promotion only possible during wartime.
The FJ-1 Fury was first commissioned in 1945, but the final version was not delivered until 1948, and never saw action in WWII. A twin-engine jet designed for carrier landings, the Fury was armed with six .50-caliber machine guns with 1,500 rounds total. By 1949, the FJ-1 was already being phased out in favor of the F9F-3 Panthers. 
Fury, the youngest officer of Mustang's staff, is often mistranslated in fansubs as Huey. Curiously enough, Huey also has connections to military aircraft. The Huey (HU-1) was a support and carrier helicopter that first saw action in the Vietnam Conflict. 
The Mi-28 Havoc was a fighter helicopter, fitted with one 30mm NPPU-28 cannon, SA-16 Gimlet AAMs, AT-6 Spiral AT missiles, and 130mm or 80mm rockets. First deployed in the late 60's. 
The E-2 Hawkeye was designed for airborne early warning, command and control. Carrying no armaments, it is classed as reconnaissance. "The Hawkeye provides all-weather airborne early warning and command and control functions for the carrier battle group. Additional missions include surface surveillance coordination, strike and interceptor control, search and rescue guidance and communications relay." 
The Nakajima Ki-84 Hayate was possibly the best Japanese fighter aircraft during the last year of the Pacific theater. The Hayate was fully the equal of even the most advanced Allied fighters, and superior in many aspects; it was well armed and armored, fast, and maneuverable. 
The P-73 Hughes was an experimental aircraft, whose designation number was skipped in favor of a more 'commercially attractive' number, and the P-75 was released instead. There was a P-73, but "it was so secret that even today there are few details available about it. The P-73 was almost as mysterious in its time as the shadowy 'Aurora' is today. However, the reason for all this secrecy was [predominantly as] a result of the neurotic personality of the owner of the company which produced the aircraft. This was none other than the brilliant but eccentric movie tycoon, inventor, and industrialist Howard Hughes." 
The P-51 Mustang was a one-man long range fighter in the patrol/pursuit category, carrying six .50-caliber machine guns and ten five-inch rockets, or 2,000 pounds of bombs. "The P-51 was the first U.S. fighter aircraft to fly over Europe after the fall of France. The Mustang destroyed 4,950 enemy aircraft in the air during World War II, more than any other fighter in Europe." 
The following are the clases of military titles in Japan, appended to the surname. Known ranks for characters are listed, and notes of fansub errors that may have been confusing. Character names in red are those that have not been fact-checked; if you see an error in a character's rank, or know of a difference in rank between the first animeverse and the mangaverse, use the site contact form to send corrections or information. Please be sure to include the character's name, rank, and the episode or chapter in which the rank was identified.
Three stripes: one thin, one large, one thin; four stars. The apparent head of the government in FMA, Bradley's title is translated variously as Fuhrer, King, or Leader. (Later explanations in the manga make it clear that Bradley's first name is "King," which parallels Mustang's first name, Roy, which has a root-meaning of "King".)
Dai-Soutou is not a common military title in recent Japanese ranking systems, but one possible origin may be that of a title used for heads of monasteries. Incorrectly translated as 'colonel' in AnimeUSA's episode 13, when Mustang speaks of the day he'll become Dai-Soutou. Also translated as 'President' in Toriyama's scanlations.
The highest possible rank during peacetime. In U.S. terms, a five-star general receives the title of "General of the" corresponding branch. This is roughly equivalent to being the branch's Chief of Staff. A fifth star can only be granted during wartime.
The commandant of East City and Mustang's commanding officer, Grumman, was a Lieutenant General. Gruman's title is most often translated as "Commander", which may be a conflation of "commandant," a position that often reflects the person's actual job (eg commandant of a military base) and not necessarily rank. (Depending on the size and location of the base, differing ranks may be assigned the position of 'commandant'.)
Hakuro's rank at the time of episode 5. Hughes' rank at time of retirement, which meant he leaps two ranks in his final promotion; normally upon retirement, an officer is promoted but only one rank. This promotion is often disregarded by officers in retirement; they usually continue to use the title of their last actual active rank, instead.
Three stripes: one thin, one large, one thin; no stars. Basque Gran's rank. In the AnimeUSA fansub for episode 13, Gran is referred to as Lance Corporal, General, and Commodore. Lance Corporal is an inaccurate translation, but the other two are somewhat correct. (Brigadier) General is the term for the US Army, Air Force, and Marines; Commodore (or Rear Admiral) is the equivalent rank in the Navy.
In Japanese terms, a general (of any rank) may be designated with an archaic title of Shogun. This was once the highest military rank, second only to the Emporer. The honorific may still be in usage to designate anyone who has reached the rank of General.
Additionally, the FMA world has five levels of generals, but the lowest rank (Brigadier) has no stars on the epaulets (tabs across the shoulders). Instead, the first star is granted to Major-Generals, which would make the Fuhrer/Generalissimo the equivalent of a five-star General.
Four stripes, three stars. Mustang is promoted to Colonel in episode 9. Hughes is promoted to Colonel around episode 13.
Four stripes, two stars. Mustang's rank when Edward reaches Central for the first time. In the manga, Hughes' is introduced as a Lieutenant-Colonel in Chapter 6.
Four stripes, one star. The default rank of all National Alchemists, even those not actively enrolled in the military. Armstrong is also a Major. Marcoh's and Mustang's rank during the Ishvar Conflict.
Three stripes, two stars. Hawkeye is promoted to First Lieutenant in episode 9. The Governer of Youswell, Yoki (episode 9), is a First Lieutenant.
Three stripes, one star. This is Hawkeye's rank when Edward first comes to Central. In the U.S. military, Second Lieutenant is the lowest rank for generalized commissioned officers. Havoc and Breda (episode 13), on Mustang's staff, are Second Lieutenants, as is Maria Ross (episode 19).
Three stripes, no stars. In the U.S. military, Warrant Officers are specialized (like enlisted), but are considered commissioned officers. Farman's rank (episode 13).
One stripe, three stars. Highest possible rank for enlisted. Fury's rank (episode 13).
Brosh, Maria Ross' partner, is a Sergeant.
To contrast between Ed and Al, Ed (in informal situations, usually around Al and other close people) uses very masculine, informal speech patterns. He also uses slang more than anyone else. Al, even when he's using informal speech, still is polite. He always strikes me as using sweet little mama's boy Japanese.
Hawkeye refers to Ed and Al with the -kun honorific, denoting her affection and their youth, despite the fact that Edward technically outranks Hawkeye. At the same time, she uses 'kimi' as a pronoun towards them, indicating her age over theirs. She always refers to Mustang by his rank.
Havoc refers to Edward as boss, taishou. Havoc is also considerably out-ranked by Edward's de facto rank of Major, so the apparent casualness may be — like Hawkeye — a way to both satisfy rank but refrain from too much deference, given that Havoc is both older and more experienced than Edward.
Armstrong refers to Pinako and Winly with the -dono honorofic, an archaic term roughly equivalent to using "Miss" as a title, in English. Refers to Edward as Elric-san or Edward-san., which may be Armstrong's means to get around rank/age issues with someone so much younger. Armstrong appears to have a strongly traditional family, and may see that nobility-etiquette as equal in politeness (but without the age issues), thus acceptable as an alternative to referring to Edward by rank (shosa).
Edward Elric refers to his brother as Al, or Alphonse, and calls Winly by name as well (no honorifics for either). He refers to Mustang as Colonel (taisa) in person; by title and name when speaking of Mustang. Edward uses title-and-name combination when speaking of, or with, Mustang's staff.
Alphonse Elric always refers to Edward as Brother (niisan), but used the diminutive term (niichan) in flashbacks, prior to their alchemical training. Alphonse refers to Winly by name, and like Edward, uses the title-and-name combination when speaking to or of Hughes, Mustang, or any of Mustang's staff.
Roy Mustang, prior to Edward gaining his National Alchemist title, used Edward-kun; uses Fullmetal (hagane) almost exclusively after title was granted. Refers to Hughes as Lt. Colonel Hughes, but drops the title during one-on-one occasions. In flashbacks (ep25), Mustang calls Hughes by his first name, Maes. Mustang uses the title-and-name combination for all members of his staff.
The section on name origins benefited from commentary and additions by Branch, Arex-kun, SV-chan, and FA Ashanthya. The section on ranks was written with assistance from SiriusJazz, Hime D., Kelly, and Saya Aensland. The information on titles and honorifics was corrected and expanded via help from Saya Aensland, Jedera, Branch, Panserbj0rne, and Lethael.
For more information on military ranks in US and Japanese military branches:
The story takes place mostly in Amestris, which is currently having minor skirmishes with Aerugo and Creta. The country is ruled by martial law, under Fuhrer/Generalissimo King Bradley. The cultural base is European, possibly German. The majority of Amestris' interest in alchemy is for military purposes.
Mount Fuji is located to the south of Youswell, in the east. Dublith, in the south, is where Izumi Curtis and her husband reside.
Side note: Amestris was the wife of Xerxes. Between Amestris and Ishvar/Ishbar is Xerxes, which was destroyed in one night. According to Greek and Persian legend, Amestris was a Persian princess who had her husband assasinated by their first-born son. Amestris continued to live well on into old age, ruling from behind the throne. She was characterized as ruthless and powerful, and Amestris' son was considered by all reports to be essentially under her thumb and helpless to cross her.
Located south of Amestris.
Located west of Amestris. May be Crete, based on the kana in the manga.
A hostile country located north of Amestris; sometimes translated as Drachna, but has been identified in the manga as Drachma. The Briggs Mountains separate Drachma and Amestris, which makes invasion for either country too much of a hassle. Side note: Drachma is also the pre-Euro currency in Greece.
A country far to the east of Amestris, across the Great Desert, with a Chinese cultural base. There are several routes to Xing. The first is a rail system that was buried in the desert; the second is a route through the Khshayarsha (Xerxes) ruins; the third is by sea. Xing has alchemy, but appears to be for medical purposes and research.
Located east of Amestris, Isshuvaru (Ishbar, or Ishvar) was annexed by Amestris during the Ishver Civil Conflict. The cultural base may be Indian or Middle Eastern, with a suggested compromise interpretation of Persian. The Ishvarites are monotheists — Ishvara means 'god' in Sanskrit — who do not believe in, or allow, alchemy. The Ishvarites' proximity to the ruined city of Xerxes (possibly destroyed through alchemical reaction) may be partly reason for their ban on Alchemy.
Many thanks to yebyosh, yuuOminae, OMchan, sarcasteak, BigFire, on the AnimeSuki Forum.
The first anime (known as Fullmetal in the tags) followed the manga with some changes, up to about the 15th episode (corresponding with chapters 24-6). After that point, the two storylines diverged. The following short and long times refer to the first anime storyline, but in general terms, the information also applies to the mangaverse/Brotherhood.
Note from Sol: this timeline was compiled by Vikki for this site, due to my own confusion about what happened at which chronological points. While I never did edit my stories to correct my confusion, newcomers to the storyline may find these timelines helpful, so I've kept them on the site. Quick version with minor details is listed first; scroll down for a more extensive and detailed version of events up to episode 13.
When Edward is younger than 4...
...4-7 years old...
...8-10 years old...
...11 years old...
...12 years old...
...15 years old...
In ep 3 we find out about Ed and Al's past.
Ed: 5-12 years old; Al: 4-11 years old.
Insert stupid ep 4 filler goodness here. Absolutely not important to the series. In ep 5, Ed and Al prove they can become Nat'l Alchemists.
Ed: 12 years old; Al: 11 years old.
In ep 6, Ed and Al go to live with Shou Tucker.
In ep 7, we find out more about Tucker and company.
In Ep 8, Winly comes to call and Ed angsts over Nina.
In ep 9, Roy sends Ed to Youswell on his second mission as a Nat'l Alchemist (his first was researching Tucker's chimera.) Nothing really important happens here, but:
Immediately following Hawkeye telling Roy that Ed is going to known as this helpful alchemist, we cut to three years later, and Ed and Al are 15 and 14 and riding a taxi through the desert, and the driver is talking about how wonderful the National Alchemist who Helps the People is. He then insults Ed by calling the Nat'l Alchemist who does this amazing stuff short, causing the driver to run off in panic. Ed and Al are now stranded in the desert, which sets us up for ...Ep 1, where Ed and Al start to set a city straight.
Ed: 15 years old; Al: 14 years old.
In ep 10, Ed doesn't want to go back to East City to report to Colonel Roy Mustang because of his failure to obtain the Stone. They detour to Aquaroya and meet Psiren ... which is completely irrelavant to the storyline. Psiren directs Edward to Xenotime on rumors of the Stone, and Ed follows her advice.
In episodes 11 and 12, Ed and Al are replaced by impostors in the city of Xenotime!
In episode 13, two manga omake are combined to make a crazy episode that's pretty much pure fun. Plot points, however, are as follows.
This concludes the anime timeline of Eps 1-13. The rest of the series through episode 27, barring flashbacks, is in chronological order.