Okay, a little preface here. Most of this information comes from Marvel.com, and the offical bio which they used to have hosted on the site. This will be...similar. Only you'll have to put up with my sarcastic commentary and quibbling over details. If you don't like that kind of thing...well, hell, why are you here?
Update: I've also got a scan of the completely rewritten bio for the latest 'Women of Marvel' edition of the Official Handbook to the Marvel Universe (2005) here, courtesy of Stacyx over at S.H.I.E.L.D. HQ. It's worth looking at, because there are some significant changes/additions over the old version.

Statistics:

Occupation: Mercenary (official) obnoxious den-mother to the former X-Force (unofficial)

First Appearance: New Mutants #98 (actually the shape-shifter Copycat, 1991), X-Force #8 (in flashback, 1992), X-Force 11 (all tied up, 1992). Take your pick.

Group Affiliation: Formerly: the NSA, Wild Pack/Six Pack, X-Force. Last seen working for Charles Xavier's newly established X-Corporation. (I should note that Domino has this horrible habit of getting her teammates killed. Really, it'd be funny if it wasn't so tragic.)

The following are Marvel's stats, not mine:
Height: 5'8"
Weight: 120 lbs. (I should note that in the real world, that's really not a healthy weight given her height)
Eye color: Blue (*mutter* Purple. Ask any real fan. It's purple.)
Hair color: Black

Powers: Marvel's been hinky with this. Generally assumed to be a form of unconscious probability altering that's not quite understood, and which makes her phenomenally lucky. Corny as it sounds, things really do just 'fall into place' for her. Well, sometimes. It certainly hasn't earned her a charmed life, and early on, her mutant status was a bit questionable. Why? I don't know, apparently Marvel thought it was 'cool.' She's never shown any sort of conscious ability to control her gift, however, which is fortunate for the people on her sh*t list. Secondary traits include her albino completion and (possibly) the characteristic 'spot' over her left eye.

History:

Early Years:
There's been remarkably little revealed about Domino's life before her time with the National Security Agency. It's generally held that at some early point in her life, the X-Man Wolverine bailed her out of Madripoor's combat pits. I'd love to give you an issue number for this bit of trivia, but honestly, I haven't a clue. I've just heard that it was 'mentioned at some point,' which is going to be a trend here. Marvel's elaborated on very few of the pieces they've tossed out over the years.

The most notable of these elaborations comes courtesy of the first Domino Limited Series ( three issues, 1997). It deals with her time in the employ of the NSA. Domino was assigned the unenviable task of guarding a man named Milo Thurman, a genius who could predict the future by analyzing past historical trends. He also had an odd obsession with Dante's Inferno. According to Marvel, it was Thurman who coined the name 'Domino' as well as the alias Beatrice. I feel it necessary to point out that A) this is a bit sophomoric and disgusting and B) that it's only really stated in the official Marvel bio. If you read the comics, all you see is a few words in bold. Not exactly proof, if you ask me. At some point, they fell for each other, and here's another point of contention. Milo was generally referred to as Domino's husband or ex-husband, but the idea that the NSA would allow their little future-predicting tool to marry his keeper is a bit of a stretch. So the legal status of that is a bit questionable, but I suppose I really shouldn't quibble over details. At any rate, the relationship went up in smoke (literally) when the yellow suited goons of Advanced Idea Mechanics (AIM) busted in, hopping to get their hands on the NSA's precognicent machine. Unfortunately, they found out it wasn't a machine at all, and when they realized they'd been duped, things got ugly. Domino managed to save Thurman's life, but the base was destroyed, and Domino along with it, or so the government told Milo.

In truth, Domino had gone on to a career as a freelance mercenary, eventually making the acquaintance of someone who would change her life irreparably--both for better and worse--namely the terrorist freedom-fighter called Cable. Along with the rest of the Wild Pack whose membership included G.W. Bridge, Hammer, Grizzly, and Garrison Kane, they worked a steady and fairly illustrious mercenary career. The team’s name was later changed to the Six Pack after threats from Silver Sable to sue over the name. Apparently, the idiocy of one illegal mercenary outfit trying to sue another illegal mercenary outfit never dawned on anyone. Go figure. The Six Pack's glory days ended disastrously when they stumbled onto a secret base of the madman Stryfe (who was also, incidentally, Cable's clone...but we won't get into that mess here) the results of which left Hammer a cripple and the members of the Pack with a deep seated hatred for Cable.

Now here's where I'm going to quibble with continuity. Early on, it rather seemed as if the Wild Pack assignment happened early in Domino's career (after all, Marvel seems to imply she's only in her thirties now) and the documented seven year gap between the end of the Six Pack and Domino's renewed association with Cable would leave a perfect opening for the NSA work. However (probably out of that need to have Milo as the originator of her codename) Marvel's chosen to shove the NSA events before those of the Wild Pack, thereby creating quite the time squeeze. I, personally, prefer the reversed order of the events, but I guess it's all a matter of how worried you are about 'authenticity.'