I have a few tips because I just did this a while ago, and I have learned from my mistakes so here it goes:
1) Make up your mind - the worst thing to do is hesitate. Once you commit to asking her, do it. I probably came off insecure because I just stood there and we were both obviously uncomfortable just looking around.
2) Casual - make it casual when you ask. Unless you want to pull a Laguna Beach thing, just keep it casual. I got so nervous because I had a plan to ask in a "creative" way, but it backfired because I got nervous...yeah...
3) Ask when you two are alone - My mates' gfs say girls wanna be asked alone because otherwise they feel trapped and will bull**** or say no, sometimes even when they mean yes. I went to ask, and one of her damn friends tagged along because she was being nosy and that added to my nervousness. It's also weird with some giggly girl standing there and I wanted to drop kick her ass across the room....spectators aren't cool man.
4) Ask in person - self explanatory.
5) Dealing with rejection - see it as how I saw my rejection: this girl missed out on a free fun night with me, so I'm going to light up another girl's night.
6) It's just prom - no biggie man. If it doesn't work out, hey it's a big ass dance and all, but you won't look back in 10 years and feel bad about this girl. You will laugh about the rejection with your mates.
Cheers man, and good luck.