She didn't intended on becoming a dancer (the nicer way of saying stripper), in fact she had gone to Sunnydale in the hopes that the Slayer there could help her with the Kakistos problem and then just with life in general.
Turns out that Buffy Summers was a liar. Girl kept saying how she didn't want to be a Slayer but when confronted with someone who did, B wanted nothing more than to be all that she could be when it came to slaying.
After the whole Ms. Post event, Faith realized that there was nothing to keep her in Sunnydale. No Watcher, no friends, no family. So she packed up her few possessions and took the first bus leaving town. (She left her motel bill with Buffy and company, she figured that they owed her something.) The first bus out of Sunnydale was headed towards LA, which suited Faith fine.
That is until she arrived and she realized that she had absolutely nothing except twenty bucks in her pocket. LA was seedy and dirty and wasn't full of a lot of opportunities for someone like her. She tried working as a waitress but it wasn't really her thing (after having her assed patted for the tenth time on her third shift, she'd poured a pot of hot coffee in a customer's lap.) Working at a call center wasn't her thing either (she just couldn't keep the smart ass remarks to herself.)
In the end, there wasn't much work for someone who hadn't graduated high school and needed the nights off. (She was still a Slayer.) So she ended up stripping for the lunch crowd at a sleazy strip bar. It wasn't much but the customers were forbidden from touching the girls, which suited Faith just fine. And she didn't need to speak to the customers (another bonus). Since she was Slayer, she could handle herself when any of the customers tried to convince her to take them on a date outside of the club.
So her days bleed into one another: she hits the club just after eleven in the morning, strips between noon and three. Heads home, sleeps for a few hour before dusk falls when she hits the streets and finds herself some vamps to slay. She goes home afterward, sleeps until she needs to get up in the morning. It's a lonely life with no safety net. Sometimes she thinks about heading back to Sunnydale and asking Giles for a second chance. By now, B's gotta be over herself by now. Yet Faith never quite makes it to the bus station, she always finds an excuse as to why today isn't the day for her to leave LA.
The truth is that it's far easier to live her pathetic excuse of a life than it is to go back to Sunnydale and deal with all of the drama that Buffy's bound to kick up. She'd rather be tarted up on a stage, taking her clothes off for business men in cheap suits than go back to where she knows she's not wanted. (It's why she didn't go back to Boston when she left Sunnydale.)