Dude, just act confident (even if you don't feel confident, act like it), and just walk up to her. When a girl is being asked out, she is just as nervous as you are likely and not even really focusing on your words. As long as you come across as a man with any confidence at all, you cross the starting line.
If you want to see a movie for example, find a time when you think she can be bothered. At the lunch line or after class for a more public thing (a girl can sometimes be flattered to be asked out in front of their peers). If you want it more private, then try and run into her into the hallway. go up to her and you can either start small talk, or if you're feeling confident, just go right for it.
Say that you thought she looked cute (find a better word than just cute) and you would want to take her out some time. Give her specific dates, and at least 2 of them. If she agrees to the date, exchange numbers with her and walk away like the boss you are. You got a date.
And if you didn't get her number don't sweat it. Failure is part of learning about life, including dating and sex. Never take rejection personally.
People say wait three days to contact, but I say fuck that. When I get a girls number, I usually text her right after I lose her sight. Text something like: "Hey, it's that handsome stud guy you just talked to". (again, make you're own dialogue up. It only works if it comes from the heart) otherwise And something that never fails: If you can get her number, you can get in her bed. But, your'e 15 so just focus on a kiss, or a feel. Don't expect anything from the girls for spending money on her. You offered to take her out, not to buy her body. If you do this you'll fuck things up, especially if she tells her friends, and she will.
Treat her as an equal, because she is. Women are not objects to be used for sex. They are beautiful gifts, that give as much happiness and respect as you give them.
If you somehow manage to get her into bed, make sure that she knows that she can trust you. When a women let's you make love to them, they are surrendering their entire body to you, a man that could crush her if he wanted. Sex is a lot more frightening for women, especially at your age. This is probably not an issue for you yet, but you should always let a women know that, while having sex, they can stop at any time. If you don't it's rape. There's no joke in that.
RESPECT WOMEN In high school I was terrified to ask girls out, and now that I'm 22, I literally ask them out without even thinking about it. But I have failed more times then I can remember.
Remember, it's better to ask her out and get rejected then to wonder for the rest of your life what could have been.
And I'll say it again because it is just the rule that I always go by: "If you can make a girl laugh, she will remember you in a positive way"
I am slightly intoxicated from this night, so some things may not make sense but whatever. Dude, just go out there and get that girl. She's waiting for you.
Any information can you tell us about her to help you?