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Go up to them with a smile, tell them to give you their hand. Then give them a spin. As long as you're having a good time they will want to enjoy this experience with you.
Damn got here before me haha. I did this a few times on Saturday and got me dancing with her everytime. One thing with dancefloor game I'll say is mix it up don't just grind with her because that's just what every other guy does, and it's happened to me a couple of times where I grind with them for a while then when I try to isolate from the dancefloor I don't get it, I'm just that dancefloor guy. What I did on Saturday with 1 girl which literally had her friend pushing me back into her was dance a bit (twirling etc) take a step back and just dance in the vicinity of her, then go back and grind (I love first grabbing their hands then twirling them into a grind with my arms around them) then after that give her a little space again and pretty much from there you can take it wherever. Baring in mind I'd say do all this in the space of a few minutes.
Another gambit for opening the dancefloor which has worked is you go up to them, dance for about 4 or 5 seconds, then give them a little playful push away and say "aww, you're a terrible dancer" turn away for a second or 2 then turn back and say "ok i'll give you another chance". This hasn't really been tested much though so it might not work as often as the other method mentioned.