They start out as “typical” elves. They live the “typical” elf long lifespans (what, 2-3 hundred years or so?), and have very strong family values, as well as being fiercely loyal to both their families and traditions. (After all, when you live for a couple hundred years at a stretch, those traditions get pretty ingrained.)
They are also incredible warriors. Not the “swift yet dainty” fighters from AD&D lore, but true badasses - think an army of Jet Li’s in pissed off, “you die now” mode, with swords.
At some point in elf history, they take over the Great Forest (which they named something appropriately elvish and isn’t on a discarded draft from the Princess Mononoke script), ridding it of the goblins, wild dire wolves (an elf ranger w/ a domesticated dire wolf, on the other hand, is a terrible thing), trolls, and other undersirables, and rule it in piece and relative isolation for generations (read: a millineum or two).
Despite the size of the Great Forest - roughly the size of Los Angeles, though with a smaller population - the cities start getting a tad crowded, as elves live for a pretty damn long time. This, combined with generations of peace (this is before humans became the imperialists of the world), leads to restlessness among the “younger” elves (insert your “he may look young, but he’s really ___ years old” dialogue here), who long to test their skills against the occasional band of orcs or testy duergar (a thread in themselves, no?).
Enter a young and, of course, charismatic prince, an imperialist in his own right, though too young to have any political clout or notable rights of inheritance. He wants to go and conquer lands beyond those of the forest - after all, what’s the point of a standing army when all you’re fighting is trolls? - but tradition is against him. Tradition says you stay home, take care of your families and the forest and its more benevolent residents (nymphs, those sentient tree guys, etc.), which is honorable, if boring.
He is a favorite among the younger soldiers, as he has a way with the sword that they envy and admire. An impromptu fan club starts, as he spars with and teaches any young warrior who asks. As he spars, he bitches (hey, he’s young), and spouts his imperialist ideologies. His sparring earns him friends who share his ideologies, and his idealism, even as radical as it is, earns him the similarly idealistic heart of a young female elf of, of course, a noble house.
And did I mention that the king was getting old? And that the ceremony of ascension was coming up? No? Well, it was. And though tradition favored the eldest son, as traditions tend to do, the young (and apparently yet to be named) prince’s ideals win him many followers. They argue vehmently that the young prince would bring the elven nation a new and unprecedented era of adventure and prosperity.
The eldest son, though not as ambitious as his younger sibling, is a very calm, composed statesman who has long since gained the favor of the ruling council, and this cements his position and quashes his younger brother’s dreams before they can start.
The younger and elder brother meet in a heated argument, with younger extolling the virtues of expansion and condemning the stagnating “older ways” and older brother (hey, look, symbolism!) arguing that a break with tradition (such as younger brother ascending to leadership) would cause irreparable harm to their nation.
Though a coup d’etat seems certain, younger brother sees the damage it would cause (though he would have won), and he and his followers (including, of course, the beautiful young noblewoman) pack up and leave, a small and formidable army in their own right.
They journey for thirty days and thirty nights and, predictably enough, end up settling in another forest (come on, they wouldn’t live in caves, would they?) hundreds of miles away from the Great Forest and bordering a great empty (though green) plain. They name this new forest something appropriately elvish, and live there for fifty years or so until human civilization encroaches upon them (or vice versa, depending on how you look at it).
In the meantime, young, exiled prince and similarly young and exiled young noblewoman become married and have a beautiful, fair-haired son. He’s set aside to grow older and more important over time.
Across the plain is a great walled fortress of a city, manned by knights, mercenary bands, and thousands of dirty, smelly humans (elves consider all humans dirty and smelly, you know?). Early attempts at communication go poorly (the lord of that city being an egotistical and, as it turns out, racist boor) and an air of general dis-ease grows between the two settlements. Time passes, skirmishes between the two grow larger and more fierce and soon there is a great and horrible battle.
The human army is immense, composed of both knights and large mercenary companies looking for glory and the doubtlessly rich loot of the (upstart) elvish kingdom. They camp several miles from the elvishly named forest, sending out various sorties and scouting parties to ascertain the weaknesses and best ways to attack the elves.
The elves, who have no calvary (early calvary attempts were met with broken necks as horses tend to not “thunder” very well in forests) employ quick surgical strikes at night, when their night vision allows them a great advantage over the humans, and when they can employ their fighting techniques to their greatest advantage (they’re better at man to man than man to horse, of course).
To best add to their advantage, they magically (or not, depending on your tastes) darken their armor and weapons so that they’re black as (insert name of really dark object/substance here), and attack to great effect. Needless to say, they win and end this little mini-war (despite their leader’s imperialist tendencies, they see little point in attacking a walled city from a field that is prone to being overrun with ponies and bearing large metal men).
As the surviving soldiers/mercenaries/random guys trying to get laid relate stories of being set upon by bloodthirsty, doubtlessly vampiric, elves, the term “dark elf” is used liberally, and the name eventually sticks.
And, just for the hell of it, elf scouts learn that the term is being used to describe them, and the new kingdom of elves quickly adopts the name as their own, as it matches their generally grouchy outlook (there are few happy exiles from the land of their birth and raising, regardless of the circumstances). Some of their people who still communicate with those in the Great Forest (even great warriors get homesick) carry word of this new moniker back and soon everybody knows them as the Dark Elves.