The Fae are collectively known by many names, one of the more common ones being Fair Folk. More traditionally, they have been referred to as the Sidhe [pronounced similar to the word 'she'], which is also a reference to their traditional Scottish and Irish homes; the barrows of the dead.
Of course, it's erroneous to say they actually live there. Those are simply where the entrances to the 'Otherworld' are found, amongst other locales. Fairie Circles, rings of flowers or mushrooms occurring in nature, are also portals to the Otherworld. Certain geological formations are also said to be entrances and exits to the home world of the Fae. Many others are rumored to exist; and there are even those Fae who can simply will themselves from one world to another, although it is only the truly powerful Lords and Ladies that can pull off that feat.
Faeries loosely organize themselves into two contrasting sides: dark and light, better known as Seelie and Unseelie. One should not make the mistake of assuming that "Light" are good, and "Dark" are bad, though, because the most important thing to remember about the Fair Folk is that their morality is in no way based off of conventional human morality.
Their idea of what is "good" and what is "bad" can not be readily connected to the common way humans tend to look at those words. It occurs, some times by incident, that Fae and Human agree that something is bad, or good, but in general, these are the exceptions to the rule; they are oddities.
Seelie Fairies tend to be nicer, and are polite and well-inclined. They play pranks, but usually not ones that are fatal, and often to teach a lesson (even if that lesson is some form of "don't fuck with me"). They some times make deals, but these deals are often meant to trick mortals into getting something they want, while giving as little as possible. A good example are the Leanan Sidhe, Faerie Women that seduce mortal artists. They offer divine inspiration, and sexual bliss, in exchange for spiritual energy. They feed off of human sexual energy, much in the same way a Succubus/Incubus does. It's something they need. Taking it slowly eats away at the humans life expectancy, all but ensuring they will die young, and possibly deranged, but... as any Faerie will tell you, everything has its price. Everything.
Unseelie, on the other hand, delight in negative emotions; they will torture children because they get a rush from the emotions. They kill, because they take glee in it. Their pranks, when not lethal, still may be crippling, or excessively harsh. In some cases, the Unseelie Faeries have a compulsion to this, rather than a clear choice; it is their Calling, their Purpose. Bogles, some times known as "bogeymen", for instance, exist almost solely to torture disrespectful and misbehaving children. They are compelled to do it, because it is what they are meant
to do. Perhaps the strongest willed may ignore it for a time; but at that point, they'll also be grappling with an existential crisis.
Even between similar Light and Dark Faeries, their morality can be pretty heavily skewed; and individual Fae may not be consistent, either. It can make them difficult to work with, to understand; and dangerously difficult to predict. The radical differences are further compounded by differences between Fae and Human biology. Stabbing a Red Cap in the chest ain't a big deal; in fact, they might laugh about it, stab you back, and hey, you're pals. But, well, humans get stabbed in the chest... and the Fae may not understand why they aren't laughing? Why don't they get back up? It doesn't make any sense to them.
Most Faeries do not bother themselves with the mortal world. They've got their own vices to satisfy, politics to hash out, battles to fight, goods to buy and sell, art projects... some times, the human world is a good "play pen" for the youngsters, keep them out of danger (relatively speaking), keep them from being a danger (some times), and give them a place where they can figure things out on their own.
Certain Faerie, however, may spend a good portion of their lives wheeling and dealing in the human world. Some are outcasts, that can not return for various reasons; reasons that are usually as different as the ones who have them. Some, such as the Leanan Sidhe, spend time amongst mortals, because their need for human sexual energy, and their desire to inspire artistic madness, make the human world an ideal home. Red Caps need human blood to prolong their lives, and so they spend a lot of time hunting 'game' in the human world.
Jumping back to an earlier topic, biology. Faeries usually appear in twisted human caricatures, with exaggerated or distorted features. Their true forms, at any rate, tend to be like that; most use Glamour in the human world to make them appear as hideously ugly, or terrifyingly beautiful examples of humanity, however. One should not mistake them for possessing human frailty, however. Most may live for technically ever; old age means little to them.
Fae are spiritual creatures of magic. It suffuses their very being, and is the source of their powers. Most Fae can shrug off harm; you can shoot them, stab them, run them over. Might hurt a bit. Might just make them laugh, because hey, that look on your face when they shrug off the blasts of buckshot? That's a funny look! But they're not invulnerable. Magic can wound and kill Faeries. Cold-forged Iron is also a common weakness to them. Weapons made of cold-forged iron tend to violently and horrifically end the lives of Faeries, and jewelry made from it is supposedly able to suppress their powers.
Charms made of rowan or certain fragrant herbs are said to repel certain types of Fae. In general, however, these 'talismans' tend to be very hit or miss, and there's no comprehensive listing of what works on what. It is also known that each particular type of Fae tends to have their own weakness; the Asrai, for instance, will melt into a pool of water if so much as a single ray of sun is allowed to touch them.
Okay, I think i got a little scatter-brained and rambling at times. I did give some embellishments here and there. This
link to Wikipedia is a decent reference, especially since their are links (Under the Faeries box) to pretty much all the Celtic ones. Like I said, run wild with it.