Boring Preface (feel free to skip): Usually I start these descriptions with a definition of what the subject is in the real world. For fae, I'm not going to do that, simply because "faerie" has been used as a catch-all phrase for so many manners of weird critter that to do some justice to the term's real significance I'd have to make this description quite unbearably long (not that it isn't already). Just one note: the word "faerie" is simply a different form of the more popular "fairy"; I'm trying to get away from its pixie-Tinkerbell connotations. Also, I've used "fae" as its plural form. I don't know if this has any precedent outside of WhiteWolf's "Changeling: the Gathering". Most importantly, this plural form is not in any way related to the word "fey", with which you might be confusing it (well, to be entirely truthful, they are etymologically related, but you know what I mean).
With that out of the way, the following definition of fae has nothing to do with how the fae are defined in mythology.
Fae are mutable creatures. While all are similar at birth, they are moulded by their environment to an incredible degree. Fae take on the characteristics of their surroundings. Fae grow to become, in fact, entirely different species; for varying types of fae can often not inter-mate. However, every new-born faerie is, once again, mutable, and can grow up to become anything. Despite this variation, they are almost always humanoid, and possess a human-like intelligence, and most possess some fairly well-developed form of language. Here is a description of some (but by no means all) of the different species of fae.
Elves are the fae of the forest. Their hair is grass, and their skin has a greenish or brownish tint. They vary greatly in aspect and attitude. The sprightly, dancing elf of common conception is found most often in the young growth of the forest edge, or anywhere where young trees flourish. The elfin leaders tend to be great, gnarled, proud beasts, and are found only amid the mighty, old trees of the deepest forest. Elves are one of the most common, and most familiar, types of fae, and they have one of the most developed societies. It is elves who are responsible for the greatest number of Changelings (which will be discussed later).
Dwarves and Gnomes are subterranean fae. Dwarves live in caves and other enclosed areas close to the surface. They vary greatly in size, "fitting" themselves to the cave they call home. They have coarse skin, long, shaggy hair, and rarely wear clothes of any sort. They have no society as such, but do have strict, ritualized ceremonies of hospitality. Those who approach a Dwarf home by the proper custom will usually find a warm, gregarious host, eager to share a meal and drink; those who enter his cave without following proper custom, will usually find a naked, screaming Dwarf, swinging around a crude stone weapon of some sort in a not-too-friendly manner. This display is usually merely that; Dwarves are not vicious creatures by nature. However, when pressed, they will defend their caves with lethal force.
Gnomes live much further underground than Dwarves. They are very small, usually no taller than a metre, and often much smaller than that. They have an insular society, and very little is known about them outside of their own circles.
... There are some other fae I'm not going to get into right now, including, brownies (plains), trolls (mountains), hobgoblins (close to human habitation, but without human interaction), and mermen/mermaids (sea). But, like I said, there's more important stuff to do, so I'll skip them for now. ...
Finally, I will briefly mention Changelings. A Changeling is a faerie who has grown up in human society. Not a sufficient description in itself, but I'll direct you to the Changeling page, which, while specifically devoted to how being a Changeling affects Morgan, should answer any questions you may have.
Related Links:
Changeling § Fairy Gifts (off-site link)