What I do
Well bud, I've been trying to master the club scene in the past few weeks. Right now I'm averaging between 4-5 numbers a night at the club. And most of them, I meet right on the dance floor. Now just approach and ask to dance any girl that's not already dancing with a guy, It's not that hard to do. You don't even need to do any small talk or anything, just go straight for the dance. Then, what I found, as your dancing, if you show your confidence and carefree attitude while just dancing, it's just as good as having a conversation with the girl.
Also, you don't have to be a good dancer, as long as you relax and just have fun with it, she'll notice. Sometimes you can do some small talk in her ear as she's grinding up on you. Or when the song is over, some girls even try to strike up a convo with you. Then at that point just do what you normally would do.
Also keep in mind that I usually get rejected more with the girls in groups, their not usually there for the men. In which case a wingman would come in handy, but I don't have a good wingman, so in that case you just have to keep trying. Eventually you do find a girl or girls in a group that end up being very nice.