Ever want to go to homecoming with a girl you like? You don't know what to do? It's simple.

[edit] Steps

Get to know her first.
Learn what she likes, that way, when you go to the dance, you know how to communicate with her.
Get your relationship with her a tad higher than a friendship.
Make sure she isn't busy the night of homecoming. Don't ask her though, it'll be to obvious.
When the time is right, ask her! Act casual. Don't be nervous. Don't blurt it out either. Just ask her, "Hey, do you want to go to homecoming with me?" If you wanna go deeper, then go for it.

[edit] Tips

Tell her how you feel about her, then she'll definitely want to go with you! Girls like sweet things like that.
Be creative. Surprise her. You don't have to ask her directly. Make a big banner and post it where she can see it.