The night elves are probably the most difficult race to roleplay well in all the World of Warcraft, which is particularly ironic considering how very popular they are. Many a roleplayer has been disappointed by seeing player character night elves who are 21 years old, who were born in Darnassus or Teldrassil, or whose mother or father is human -- all of which would be next to impossible according to the actual lore of the game. The only way to make things like this is to change the lore to suit your own preferences, or to rely on cliche devices such as time travel and special magics which really go too far into the realm of the abominably self-centered Mary Sue.
Night elves can also be difficult to understand, and full of contradictions: they can be over 10,000 years old, and yet they often do not possess the vast wisdom that would seem to come with such an age; they are deeply connected to nature, and yet they sometimes act without the blessings of nature; their women are supposed to be very fierce warriors, and yet their animation in the game has them bouncing up and down like teenage girls at their favorite boy-band concert.
And yet much of this is just the sort of thing that draws people to the night elves. There's a youthful passion combined with ancient grace and sadness that many roleplayers just love to get into. Also, for those who love to develop long and complex background stories for their characters, there is a great deal of history about the night elves' ancient past which can serve as good inspiration for many of your own character's life events. We won't go into every detail of ancient history today, however; instead we'll cover the basics that you'll need to know in order to start out with a night elf that fits in the Warcraft story, and direct you to some more resources if you'd like to make one with a really deep and complicated background.
The most important thing to understand about the night elves is that they are old. They are the only player race native to Azeroth with a lifespan greater than five hundred years.
Many eons ago, they were merely a race of nocturnal humanoids, presumably short-lived and savage just like everyone else, who just happened upon the most powerful magical spot in Azeroth, called the "Well of Eternity." At that time, the world now known as Azeroth was just a single continent called Kalimdor, and the Well of Eternity was at its center, pulsating with magical power so fierce that no one who entered it could hope to survive. These energies transformed the creatures who came to live nearby, granting them power, long-life, and eventually immortality, changing them into the "kaldorei," or "children of the stars."
This beginning is in many ways the cultural foundation that still defines the night elves, even after the Well of Eternity had been destroyed and their immortality lost forever. Even now, they retain an air of mystery, and view themselves on the scale of eternity rather than the mere lifetimes of mortal races. For them, the loss of this immortality has been a bitter pill to swallow, and many still do not view themselves as equals to the other races, thinking of "old age" as something that happens to other species.
The second most defining characteristic of the night elves is their distain of all arcane magic. They view this magic as a dangerous and corrupting power, ultimately evil in its essence, and shun its use completely. They tend to look upon humans, orcs, and other people who attempt to manipulate this power as fools who do not realize the danger they are playing with.
The irony that they themselves became who they are through their association with the most powerful source of arcane magic in the world is surely not lost on them, as this made them uniquely poised to witness the ultimate effect such power can have on people.
Ten thousand years prior to the setting of World of Warcraft, the demons of the Burning Legion saw the magical energy of the Well of Eternity radiating across the vast expanse of the magical universe, and immediately developed plans to seize it for themselves. They corrupted the ruler of the kaldorei, Queen Azshara, seducing her with promises of power and convincing her to open a gateway for the demons to come and destroy everything in ancient Kalimdor.
This "War of the Ancients" that ensued between the demons and those elves who resisted this invasion culminated in the destruction of the Well of Eternity, and the sundering of the world into two separate continents: the western one, which retained the name of Kalimdor for the night elves, and the eastern continent, which they left to the other races of the world. Between these two continents raged a perpetual vortex of energy called the Maelstrom, where the Well of Eternity had once been.
Although night elves were not completely destroyed, the leadership of the night elves was shattered, and many conflicts and difficulties arose as they tried to rebuild their society. In addition, it soon became clear that not all of the magic of the Well of Eternity had been lost. Some of its waters had been saved and used to create a new fountain of power at the top of Mount Hyjal, but this time they built a gigantic "World Tree" called "Nordrassil," which grew out of it, absorbing and purifying its power so that it could no longer be tainted by the demons. With the help of the dragons, the enchantments and blessings of the World Tree became strong enough to stave off another invasion by the burning legion for ten millennia until the events of the Third War, just five years before our game begins.
As far as nature is concerned, while tauren are very much connected to the earth, the night elves are more connected to the sky. The tauren are a plains people, while the elves are forest-dwellers, who look up to the sky and worship Elune, the goddess of the moon, as the protector of their people. In fact, the demigod known as Cenarius was actually born to her and lived among the kaldorei for many millenia, guiding them and teaching them the ways of druidism.
Men in particular were drawn to follow Cenarius' teachings, and revering all the spirits of nature, and taking on their forms to protect the natural system. The green dragon Ysera was the protector of nature, and she called upon these druids to abide with her in Azeroth's parallel world of nature energy, the Emerald Dream, in order to help maintain the natural balance of life.
Women were largely left to run the society of night elves as priestesses, or defend it as warriors and hunters. The arts of prayer, scholarship, and martial defense were the primary pursuits of the night elves, since presumably all their material needs were provided for by the druidic magic of nature, the World Tree, and the surrounding forests that had become so central to their existence.
The effect of the War of the Ancients upon night elf society was so severe that they never lost their constant vigilance in protecting their precious World Tree, and kept their source of power secret for all these millennia by sealing off their borders to the rest of the world. But although the other races of Azeroth had largely forgotten their existence, the demons remembered, constantly coveting the power they once came so close to taking for themselves.
Ages of planning came to fruition for the demons when the events of the Third War began to unfold in the lands of the humans and the orcs. When the orcs came to the western lands of Kalimdor, the demons' successful attempt to control them once again made them into a deadly threat to the night elves. Imbued with demonic energy, the orcs rampaged into the night elves' forests in search of lumber, and destroyed anyone and anything that stood in their way. The demigod Cenarius was one of the casualties of this conflict, and his death made the orcs into permanent enemies of the night elves.
As events unfolded, however, it became clear that there were greater demonic powers at work than just the corruption of the orcs, and this time the night elves could not hold off the demonic attacks by themselves. Although the different races of Azeroth banded together in one great battle against the demons, it seemed that the forces of evil would succeed at last in taking the remaining energies of the Well of Eternity, until the night elves made the final sacrifice and destroyed their World Tree and all the magical energies it contained, burning up the leader of the demons with it.
Since those deeply traumatizing events, the night elves have been a bit confused about who they are and what they want. The new leader of the druids insisted that they plant another tree, called Teldrassil, in an attempt to regain the immortality that they had lost in the war against the demons. This, in spite of the fact that the dragons would not agree and it could not be enchanted with the true blessings of nature.
For the first time, the night elves must now find a place for themselves in a global society. They no longer have such a dire secret to protect, nor do they have many of the benefits and special status that came with being the protectors of the world's most magical spot. Their most cherished demigod is dead, and other races do not seem to appreciate the cherished way of life he had taught them. They are at once ancient and wise, yet temperamental and as yet unable to fully adjust to the new state of the world. And finally, they must begin to accept that after all these ages of superiority and deathlessness, the specter of old age and "natural" death, must eventually come to them as well.
A side note on lifespan and maturity
The night elves have this really tricky problem which I personally find hard to deal with. Even their youngest adults are supposed to be about 300 years old, 3 times as old as the most ancient of humans. To some, this means that there's really no space among night elves for the "average joe" type of character -- they say that every single one of them has to be ancient and brooding about all this serious stuff I've just been going on about.
Well I say "Phatooey!" to that. In my opinion, Blizzard gave night elf women that cutesy bounce animation for a reason, and that's so that we wouldn't take anything in the game tooooooo seriously. Granted, I don't like that particular animation much, but that's beside the point. Some night elves can and should have a rich life full of all the things that make life livable for any sentient being, and it makes sense that some of them will deal with their loss and tragedy through humor, the same way that humans do -- even if they're 15,000 years old, maybe even moreso then.
However you play a night elf, though, keep in mind that they are pretty old, even for young people. Just about all elves over the age of 300 look to be all about the same age (the equivalent of a human in their 20s) and are only now starting to age. (Technically none of them should know this yet, I think, but in about 4 or 5 hundred years they're going to start getting old and dying -- but that doesn't really matter to us as far as our roleplaying is concerned -- just don't try and make an old and wirey night elf character, as such a one does not exist.)
Your character may have spend most of the last 300 years playing games, digging in gardens, and studying books like any kids you might know about, but they still spent three-hundred years doing all that, and they're not going to be just like any old 18 year-old human you might come across.
Again, don't take this too seriously though -- go ahead and try to imagine what several hundred (or even several thousand) years of life might be like as far as your imagination can take you, but don't feel ashamed if you can't really go all that far. Nobody has a clue what such an age would feel like, so I say pick whatever conclusion about it seems to make the most sense to you and run with it. After all, who out there has the experience to prove you wrong?
For more information about night elves, check out WoWWiki's information about them, as well as Dramatis-Personae's quick-start night elf page. If you're interested in novels, then consider reading the War of the Ancients stories, as well as other books about night elves. Also, check out this silly thread about night elves' maturation rate and just interpret what "maturity" means in any way you like.