I went to go see Louis CK live a few weeks ago. During it he said that asking a girl out is an extremely brave thing for a man to do because every part of his brain is telling him to shut the forget up and go away, even if the situation sounded perfectly logical and simple beforehand.
And he's right. It's not as hard as your brain tells you it is, because your brain likes to screw you over. If you just, say, ask for her number at the end of a conversation or something casual like that (though I don't know if that's casual for your age...) she'll probably give it to you, especially if she actually knows you. Getting her number is a way to get closer to her without straight-up taking the chance of getting a yes or no.
Note that most of this opinion is less than 24 hours old.