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The series, and the movie for that matter (which takes place directly after the series) are absolutely phenomenal and will forever remain my favorite anime.

Very well written, Kris, but you forgot a whole ONE thing, which is really damn impressive:

There is a path that one much follow when PERFORMING alchemy, a path that must always be followed unless there's some grand ability or otherwise motion that allows you to skip one of the three steps, like in Maria's case.

Bare in mind, you MAY stop at the second step, though it's usually frowned upon (it was the signature technique of the "rogue villain" in the series, and the main character did it once as well) as it leads only to death.

I. Assess the item and memorize the components of said item.
II. Deconstruct the item (Keeping in mind what Kris said: Energy and even matter are never lost, only displaced)
III. Reconstruct in to the desired new item.

For example, say you have the following ingredients (this I learned in high school):

Oxygen (65)
Carbon (18 )
Hydrogen (10)
Nitrogen (3)
Calcium (1.5)
Phosphorus (1)
Potassium (0.35)
Sulfur (0.25)
Sodium (0.15)
Chlorine (0.15)
Magnesium (0.05)
Iron (0.0004)
Iodine (0.00004)

With those components, you could create a human being and really piss off God. But, you'd need the exact amount of each component (the numbers in the parenthesis represent how much of each component is in the human body, by weight) or you'll get some ******** up monstrosity. Scientists every day try to replicate human beings.

So, I basically just laid out step one, given I just analyzed the entire human body for you. So, the next step would be to find...well, let's say a human! At that point, you'd use proper methods via transmutation circles to deconstruct that body, and with that same circle you'd pull it back together, letting the transmutation circle act as a table for the puzzle you're now solving as you put the pieces where you want them.

There's a bit more to it than this, but given it's one of Kain's specialties, I don't want to give EVERYTHING away. I figured I'd help Kris a bit in his contribution, though.

The Creatures of Alchemy: Homunculi and Chimeras

Alchemy, of course, is more or less the work of God in that it's all about creation. Since the dawn of time, in one way or another, man has always performed and tinkered with alchemy, and thus we were given new inventions. Most people tend to associate alchemy with potions, or even further, simply pharmaceuticals; combining potions or concoctions to create brand new ones. People also tend to associate alchemy with transmutation circles, which more or less begins to reference it as a black magic. But, needless to say, it's obvious alchemy's been used to create some amazing medicines, and other valuable tools in the world.

Then, there are the alchemists that can't handle simply doing God's work, but must spit in His face while they're at it. This is in reference to the creation of two beings that can only come to be through man's own sick intentions, through the art of alchemy: The Chimera, and the Homunculus.

The Chimera

When most people think of a chimera, their minds are drawn more towards the mythological beast composed of a lion's head, a goat's body and a serpent's tail. There are endless variations of the creature, and in the end each of them could essentially be correct. A Chimera is nothing more, and nothing less, than several creatures fused together in to one new creature. The creation of such creatures has been identified to need transmutation circles and a great deal of practice and wisdom. Chimeras are highly frowned upon, given they destroy God's work and turn it in to man, and beyond that the creature usually ends up suffering a great deal of pain given they were formed improperly, if there even were a proper way. True alchemists always put it on themselves to put the lives of these creatures to an end, not for anyone's sake but that creature's and the pain they suffer.

The Homunculus

And so it was said that God created Man in His likeness. And so it was said Man created the Homunculi in their image. And so it was said alchemists became Gods in their own sense. Though, unlike Chimeras, the Homunculi come with a whole set of rules and restrictions to them, regardless of ability and wisdom.

-The Homunculus can only be made using the dead.
-The Homunculus will take the form of that dead person.
-The Homunculus will be born with a Ouroboros (*I).
-The Homunculus will take a new personality/soul (*II).
-The Homunculus cannot be made without a personal item of the dead being's nearby, and the Homunculus will be rendered powerless when near this item (*III).
-The Homunculus can function without this, but in order to function properly and to it's full extent, the Homunculus must feed on life and souls to maintain itself.
-The Homunculus cannot use alchemy.

*I: The Ouroboros is a tattoo, or marking, engraved in to the flesh of the Homunculus that identifies it as such. The creator or the Homunculus can also control the Homunculus using this alchemic symbol.

*II: Though the soul will be new, it will have the old soul's memories. The Homunculus will not understand them, nor the dreams they will be cursed with, but if their will is strong enough, a Homunculus can rid itself of it's old personality completely, or just the opposite, in can become who it once was.

*III: The item can be anything from the bones of the person to a personal trinket. Either way, this is the item they will be born from, and thus the item that will end them. The item is usually kept on the creator.

The reasons for someone creating a Homunculus can vary, but most commonly people wish to bring their loved ones back from death, or wish to create an army. Sadly, what they create, at least in love's case, is never what they want. In the case of an army: The Homunculus does indeed have free will, and mistreating it can lead to one wrong move being your downfall. Most Homunculus are also born with specific powers, usually dealing with exactly what they were created for. For example, Fullmetal Alchemist featured the following Homunculi created by Dante:

I. Lust; able to extend fingers which were as sharp as a blade. Her Ouroboros was on her chest.
II. Gluttony; could eat anything given acidic saliva. His Ouroboros was on his tongue.
III. Envy; could shapeshift and had super-human strength. His Ouroboros was on his lower back.
IV. Pride; he could see all possible outcomes of every action, and in the end, read someone's movements before they would happen. His Ouroboros was on his left eye.
V. Sloth; she could become water. Her Ouroboros was under her left shoulder.
VI. Greed; he could fiddle with the amount of carbon in his body to harden it in to an impenetrable material, most likely diamond. His Ouroboros was on his hand.
VII. Wrath; could use alchemy given his right arm was that of an alchemist's, as was he left leg. His personal powers were Godly strength and agility. His Ouroboros was on his right foot.

Known Chimeras in FoM:
Tedd; AKA "The Beast." Kain's ultimate creation made from nearly every animal he could get his hands on, along with several different materials aside from animals. In the end, Tedd and it's lost brother, Todd, were created. Tedd was given high intellect and can communicate as it sees fit, and it's powers are nearly endless, though at the same time very limited. Unlike most Chimeras, Tedd feels no pain from it's fusion, given that Kain worked with another lost alchemist and Tedd itself to fully construct the monster.

Known Homunculi in FoM:
I. Maria - (Classified to Kris' liking)
II and III - Mother & Father. Kain used his own parent's heads, which he severed centuries back to bring them to their dooms his own self in order to make things right. Both Mother & Father have had their memories of that past life completely erased. Their powers vary quite a bit, and both are quite grotesque.