It depends on how much you want to go with her, if you REEEEAAAALLY want to go with her, then you would get one of her favorite flowers and ask her, maybe with a note around the stem. If you don't feel like buying the flower, then a simpler way is writing a note to her, like in class. If you want to ask her in person, you go to a place with not many people and ask her. If you want to just hear her reaction, call her and ask. But calling is the worst way.

for some reason, prom is like the BIGGEST THING EVER at my school
some guys go all out, like calling a girl to the office and meeting her there with a huge bouquet of roses, making a trail of rose petals out her car and having the office call her about her headlights being on and meeting her there with a bouquet, but here's the winner:

first, let the parents know what you're up to, because it would be super creepy if you just randomly started doing this.
take either candles or christmas lights and spell out "Prom?"
wait until it gets dark, but not pitch-black dark and turn them on. just make sure she's not at the window. then call her and tell her to look outside.

believe me, she will love it.

wait till a rainy day if you can, and out of no where, go to her house get her to answer the door, pull her outside and kiss her, and ask her to prom, ( if your dating her ) if not, and you dont know her toooo well, you should just bring up prom, and say you always wanted to go with her since you met her. those should work. :)

get a bunch of christmas lights and light up a park. have a sign saying prom made from the lights. this is pretty tedious but it works great