General

shove a bunch of female toys in her locker saying "Dil-Dont forget you should go to prom with me."

"Hey girl, that dress would look so much better accelerating towards my floor at 9.8 m/s^2 "

LOL! This question brings back memories.
I remember this kid back in highschool made a lengthy maze of riddles and eventually the last note was in her classroom, so when the guy came into the class to pop the question, he got turned down in front of everyone. I guess it was a sweet idea, but he looked like a moose so...there's that.

At lunch, go to where she is sitting and loudly ask her "May I have the honour of going to prom with you?"
Cuz
1. girls love confidence
2. girls love feeling that they are special snowflakes

dont ask her to the prom. it is a long boring experience. instead play some maplestory with her or RP in takistan life (if you are already whitelisted)

Keep it simple retard.
Just go up when she's alone and ask if she wants to go. "Do you wanna go to prom with me?"
The more you think about it the more nervous you'll be.

Basically asking a girl to prom is like asking her for sex. Bring condoms and beer.

As a girl, my advice for you would probably be to talk to some of her friends and see what she might like (if you can't talk to her friends / her friends don't like you, you're in bad luck and should probably not hope for much, sorry). Every girl has different interests, different things that she finds thoughtful or romantic-- and some girls don't like romantic things-- which is why if you don't have any ideas, you should ask her friends. Her friends can give you some ideas and help you plan, but you should ultimately be doing most of the thought and work since you're the one who's asking her to prom. Clever ideas are really neat, but I'll bet you a promposal with things that she likes is gonna be more attractive to her.

serenade her with a dance. I would suppose I would dance for her but you can also sing or get a lot of signs for her to read with flowers. I would recommend a video to record to her about how much you love her and after the video, come up behind her and get her flowers XD

Aight I'll try to help you out, but given the fact that I haven't gone yet I'm not so sure how much this will help:
Step 1: Try to get her in a private place with either just her or a couple of her friends (you don't want to make her feel pressured into saying yes just so that she doesn't get harassed by complete strangers for rejecting you)

Step 2: Go up to her and just say it with confidence. Give her a little gift (flowers, chocolate, etc.). Just don't appear nervous and you'll be fine.
Also, don't make a big show out of it (like doing some big dance number or something). I always hear stories of girls who say yes just so they don't look bad and then tell the guy no privately through text. Only do something like that if you're already dating or know that she'll say yes.
Hop I helped. Though I'm not sure I did.