There are lots of things you can do. Personally, I would recommend not doing something very typical e.g. "Hey, wanna dance with me?", it's a club, not a prom.
Before approaching her
First thing you will need to do is inform her of your presence. Try to have eye contact to her, with a slight smile. Once that's done many scenarios can happen.
- You and her will keep having eye contacts with each other.
This most probably means that she is interested in you. After a couple of eye contacts, you can approach her. Having too many eye contacts is simply risky, because time passes. She may leave or get asked by another guy. That's the reason you need to be efficient. Enough eye contact(s) for her to know your presence and you get an idea of her mood but not too many and risking of losing her. By having some looks with each other before you come close to her, she will feel comfortable, secure and somewhat familiar with you, instead of you going unexpectedly or randomly to her.
- She never looks at you again
Although not certain, she is probably not very interested. Of course, you have nothing to lose if you still approach her.
Depending on her look during your eye contact(s), you will get lots of insight. Sometimes it will be deadly obvious that she wants you to go talk to her. Try to decrypt her face look and prepare accordingly.
This is the hard part. Even if you both had multiple eye contacts, you can still ruin everything if you do this wrong way. Since you are in a night club and the sound is strong, you need to keep the talk low. Comparing to a pub setting, you can't invest much in talking. Of course you will talk -and it will be important what/how you say- but not too much.
Again, this is a dance club and she is dancing. You will need to be in a dance mood also. Approach her by looking only her and extent your arm nicely with a smiley face without saying anything. You just asked her to dance with you. If she gives you her arm (YEEIII!!), pull her gently and nicely out of her friends circle and go a little bit further to dance (not too far away, that would be creepy, just 1-2 meters - she needs to feel she is safe close to her friends). You have started dancing with her! Of course, how you dance is up to you. Assuming she enjoys dancing with you, you can then try to touch her in a nice way i.e. placing your arms in her waist, be gentleman and respectful. Enjoy the night! ;)