We know next to nothing for sure.
* Erm. She's from Boston.
* Her mother was an alcoholic. She didn't get Faith a puppy, but it's important to note that she did take the time to give her daughter an affectionate nickname. Since Faith also mentioned jumping into a quarry lake, its safe to assume that Mrs. Faithsington either had little interest, or little control. Mommy's now dead. Never mentioned a dad. It's implied that he was either absent, or somebody new from week to week. She does have something of a parent related obsession. In This Year's Girl, not only do we see that her most treasured dream is just a picnic with the Mayor, but that's not all. In many ways, Buffy's the only one who gets Faith. In many others, she doesn't get her at all. She knows Faith is going to go after whats most important in the world to Buffy. Buffy assumes that Faith would consider that to be Riley. Faith, without hesitation, goes after the person she'd consider the most precious of all. And that's- who else?- Buffy's mom.
* Faith has an in depth knowledge of S&M, right down to safety words and what could be interpreted as autoerotic asphyxiation. I consider the following scene to be yet another S7 continuity blunder, but lets run with it just for the sake of interest. She tells Spike about the guy-with-the-Bullwhip (GWTB) and the role play. Now, Faith has been in prison for nearly three years by this point. Before that, she was in a coma for 8 months, sending us back to season three BVTS, when Buffy was turning 18, and Faith was younger. Which means that Faith was engaging in hardcore bullwhip-and-all S&M when she was at the very most, 17 years old.
* As one of my IMDB buddies pointed out, despite Faith's demeanor and attitude, she never actually said she came from a poor background. For all we know, she's from a well off family and she's just a runaway with rock chick aspirations. However, she does give the distinct impression that she was quite capable of kicking various forms of ass long before the slayer thing came along. It's been argued, but never solidly, she was indeed in a gang.
Her stories about the preacher and the gator wrasslin' could well have been made up to impress the Scoobies. For all we know, Faith isn't even her real name. Nothing she says, or in many cases, does, can be taken at face value, so it's very hard to know for sure.
She's extremely reluctant to talk about her past. She only willingly does so twice, once when she's sure that Buffy is about to kick it, and the other time in her last conversation with the Mayor, when she totally trusts him. Which would suggest that she either did something, or had something done to her that would undermine the rock bitch image she works so hard to maintain. Her obsession with control and domination is generally put down to being her way of reversing/ avenging whatever trauma was inflicted on her. I've heard some well made arguments to the effect that Faith's attitude to both men and sex are evidence that she was raped at some point. Despite her attitude to sex, I don't agree that this was the intended interpretation. To Faith, Sex and Violence are interchangeable, so for her, being unable to prevent the death of her watcher at the... em.. hooves of Kakistos, and rape could have an equivalant effect. As for her distrust of men- She doesn't trust them. Yeah, but she doesn't really trust anybody except parent substitutes (Her previous watcher, Gwendolyn Post, the Mayor, and eventually Angel) Her attitude towards them is an extension of her need to be ...erm... on top, both in slaying and laying.