Ask her. It's painless, I promise. Don't be weird and don't do anything over the top, just straight up ask her. When you're there, do as CB suggested. Be casual. If you need a tux, they're easy to find cheap at thrift stores and places like that this time of year or you can rent one. Ask her sooner rather than later because she needs to get a dress and that's a fucking process, trust me.
Don't consider it a date. If you like her after prom, ask her out. If you don't, don't.
Serious advice: if, as I assume, you and/or her have never experimented with alcohol or drugs or anything like that, *don't*. Prom night is basically the one night where you're gonna get caught.
Less serious but equally important advice: if you suck at dancing, do it anyway. Just let loose. You'll have a lot more fun with her if you're not trying to come up with excuses to stay off the floor the whole time.