How to Ask a Girl Out on a Date
First, get to know herIf you just come out and say: "Hi, do you want to go out sometime?" not good. She'll probably think to herself "ehh, no, you don't even know me." Instead strike up a conversation and remember to keep things light, talk about things you both have in common like school, music or TV shows you both watch. Find out what she likes, what she does for fun, then decide if you like her and want to see her again.
Sell yourself (a little, not too much though)When you're getting to know her, make sure to listen closely and mention things about yourself that she might like. Don't brag though, play it cool and be yourself.
For example, if you ask her what music she listens to and she says Coldplay, you can say you are learning to play one of their songs on the guitar or if you don't play the guitar you can say that she might also enjoy another band called Radiohead. This shows her that you have things in common and you learning the guitar or sharing your musical knowledge might impress her and motivate her to know more about you.
Find out if she has a boyfriendOnce you know each other a bit better, you can ask her if she's seeing (dating) anyone. One way to find out, without asking her directly, is to ask her friends or assume she already has a boyfriend and say something like: "What are you and your boyfriend doing this weekend?" If she says this and that then you know she has a boyfriend, however, if she corrects you and says that she doesn't have a boyfriend then you know she's single.
She will probably see right through you though, I think it's better to be direct and just ask her if she's seeing anyone at the moment. Plus, this way it lets her know in a very small way that you are a little bit interested so when you do actually ask her out, it's not a total shock. Caution: this should not be the first question you ask her, step one is getting to know her first. And if she has a boyfriend, don't ask her out.
Ask her outOK, so you've spent some time getting to know her, you like her and she doesn't have a boyfriend, ask her out. Make sure to do it in person and try to do it without friends around if you can help it. (Phone is ok but you won't get to read her reaction.) Think back to the things she said she liked and try to work that into you asking her out.
For example, imagine she told you she really liked art, once you get the conversation going, you might say: "Hey, I know you like art and there's an exhibit I was planning on checking out this week, I think you'd like it, we should totally check it out if you want." This will show her that you actually paid attention when she was talking and is sure to score you some points. Or you can be more direct and simply say: "hey, do you want to hang out sometime?" that can also work.