Gnomes are probably the easiest race to roleplay in World of Warcraft. They have a strong (and mostly accurate) stereotype that people just get instantly, and there's a childlike "blank-slate" quality about them that means that they don't have to have complicated backstories.
In fact, you could define the gnomes as a race without a history to speak of. They are so very curious and inquisitive that they ask questions about everything, that they try to unravel any mysteries they encounter, and consider their personal life stories to be of little account. They've written tomes upon tomes on the inner workings of multi-polar data transfer relays and eletro-magnified parallel power circuits, but it never really occurred to them that they should write down the history of their species. They are a people always looking into the future, and whatever passes beyond the infinitely precious present becomes lost to them in the unseen reaches of the past -- out of sight, out of mind.
That's not to say they have no memory -- they make use of their superb memories in carefully constructing their world-renown masterpieces of technological craftsmanship! Rather, it would be better to say that their minds only serve up memories relevant to the inquiry at hand. So if the orcs paved through azeroth a while back and destroyed everything in their path, well that was bad and all but it was a long time ago and who wants to hold a grudge? If the monstrous troggs came from the bowels of the earth and destroyed their cherished technological city of Gnomeregan... well, they'd love to get it back, but it's no reason to be unkind or uncheerful!
I'm partially overstating the forgiving and forgetful nature of the gnomes when it comes to Gnomeregan, because, although they do remain cheerful and friendly in the face of such a devastating disaster, they remain resolute in trying to get it back. That city was the whole world as far as the gnomes were concerned, perfectly suited to all their experiments and calculations.
They had been living in their underground city of mechanical wonders for generations upon generations, where they peacefully planned and carried out their experiments under the rulership of their elected High Tinkers. During the Second War, they aided the dwarves, high elves, and humans in their struggles against the orcs by supplying flying machines and submarines. But during the Third War, the gnomes withdrew from the Alliance for reasons that the Humans and Dwarves could not understand at the time.
Within Gnomeregan, however, the gnomes were dealing with a crisis of unprecedented proportions, a drama of dastardly deeds, and a bastard's black-hearted betrayal. A foul greed and utterly ungnomely ambition had been festering in the gnome known as Sicco Thermaplugg for many long years, as he weaseled his way up the ranks of the gnomish society. Although he was the closest friend of High Tinker Mekkatorque, he plotted all along to ruin his leader's reputation and usurp his position. Thermaplugg conspired a series of events which led to an enormous army of evil troggs bursting up from deep underground through the city's defenses, rampaging through the city and laying waste to everything in their path. Although the gnomes fought bravely, they were much smaller than their monstrous invaders and not at all prepared to fight inside their peaceful home.
Preying on the High Tinker's indefatigable courtesy and naivete, Thermaplugg dissuaded him from calling upon their friends in the Alliance for help, pointing out that their fight against the Burning Legion left them with little resources to aid the gnomes. He further used his trickery and guile to convince the increasingly desperate High Tinker Mekkatorque that the only way to save their city was to open the vents to the city's radioactive waste tanks and irradiate the city. Perhaps the High Tinker was too distressed to think clearly about the consequences of such an action, or perhaps he simply placed far too much trust in the assurances of his false friend, or perhaps both. But in the end, he and a small remnant of his people were lucky to escape with their lives, their health, and their sanity, to live as refugees within the dwarven capital of Ironforge.
Whether Thermaplugg was trapped inside Gnomeregan against his will, or chose to hide there in anticipation of his victory, even the madman himself may not know. All the gnomes who were trapped inside certain sections of the city became afflicted with hideous leprosy and descended into madness, if they were not killed by radiation sickness or by mutated troggs first. Although many troggs had survived the radiation and still infested much of the city, Thermaplugg declared himself High Tinker of Gnomeregan and ruler of all the gnomes, twisting his remaining people into insane shadows of his own paranoid and demented mind.
"An arclight spanner in the hand is worth two in the gyro-matic auto-expanding toolbox!"
Although, as we have seen, gnomes do fall into megalomaniacal lunacy from time to time, by and large they are far too busy discovering the mysteries of the universe to be troubled with little things like who's going to have power over whom. Their natural curiosity is founded on an unshakable belief that all questions have an answer, even if we do not yet have the means to find it.
Of course this mindset lends itself towards the acquisition of more and more knowledge wherever there is scientific knowledge to be found. Gnomes excel as mages, warlocks, and sneaky rogues, and even as warriors with more brains than brawn. Their mindset is ill-suited towards more ambiguous professions such as those of the druid, shaman, priest or paladin, although some gnomes do profess a great reverence of the Holy Light. Some say that gnomes are not religious, but I would say that they simply do not let religion be religion -- they have to know how all that faith stuff actually works when it comes down to the nuts and bolts of it, and they get too bogged down in this investigation to realize that such spiritual things aren't made of nuts and bolts at all.
"I tinker, therefore I am"
Gnomes are, of course, most famous for their technology, and have been rivals of the goblins and their technology ever since anyone can remember. This rivalry has ever escalated into any sort of fighting, of course -- the gnomes are too good natured and the goblins are too economically minded for either of them to think of fighting about engineering methods -- but nonetheless the two forms of technology contrast sharply with one another.
Goblins are a short-lived species who rely on wild inspiration and lucky improvisation to get things invented. If a goblin can't think of a practical marketing strategy for his invention, he'll just toss it on the trash heap and start over with something else.
Gnomes on the other hand, often spend more time on planning a scientific endeavor than on actually undertaking it. Even a measly mechanical squirrel may have pages and pages of blueprints and plans detailing every aspect of its manufacture. Gnomes persistently pursue every train of scientific thought to its ultimate end, whereas a goblin would scream out loud at the mere thought of thinking so much.
Although engineers usually take the path of tinkering associated with their race, it is not uncommon for a gnome to take up goblin engineering even if just to find out why goblins find it so interesting. Nevermind that so few goblins live to tell about why it's so interesting -- the gnome still wants to know.
"My pheromone emission analysis suggests that you and I share a 97.43% compatibility rating, and leads me to the inexorable conclusion that we should explore our mutual interest in our common inquiries with the ultimate intention of perpetuating our species in accordance with our natural biology!"
A gnome life is, like that of a dwarf, long enough to enjoy the relentless pursuit of knowledge, but short enough not to get boring. While the dwarves pursue the mysteries of the past, however, the gnomes only have eyes for the future and the present. They both mature at about the same rate, becoming adult at 40 years, though the gnomes enter middle age a bit earlier at the age of 100 or so, and may die of old age as early as 150 years old. 200 is considered quite old, though a few gnomes have managed to survive up to 500 years, possibly just by wanting to scientifically prove it was possible to do so.
Any gnome alive today would have grown up in Gnomeregan, of course, surrounded by the quest for knowledge on all sides. Upon reaching adulthood, he or she would have chosen a new surname as a mark of some personal achievement or trait (such as Manamilk, or Whistlespring). Some of the more mature gnomes might have participated to some extent in the Second War roughly 20 years ago, but a youthful gnome would have just reached the spritely young age of 45 or 50 or so when chaos broke loose in Gnomeregan. That experience was very likely the worst of your dear gnome's life, but he or she lived through it and sees no point in dwelling on the unpleasant things of life. Some gnomes, such as High Tinker Mekkatorque himself, bend all their energies towards retaking their home from the leper gnomes and the troggs, but many others have accepted its loss due to permanent radiation and have already moved on to other avenues of inquiry, seeking understanding of previously unimaginable mysteries. To be a gnome is to question the very foundations of reality, and live to make an invention out of it.
For further reading about gnomes, check out WoWWiki's information about gnomes (though I found some things there to be inaccurate or confusing), as well as Dramatis-Personae's short summary of how a gnomish adventurer's story would start. Even though there isn't much lore about gnomes, they are possibly the most fertile ground for the imagination of all the WoW races, and require the least management of tricky dates and timelines. If you don't know much about WoW lore and have an appreciation for silliness and cuteness, gnomes are the race for you.
[Edited to add a little bit about gnomish surnames]