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Casually talk about stuff she likes and dislikes. Start by just having conversations with her. Ask her about her siblings or other little things. For example, "How are Jimmy and Sarah doing?" or, "That blue shirt brings out your eyes." Girls like it when you remember little things.  Find out things you have in common, like a favorite band or sport. That will give you a common subject to talk about. If you go to school together, walk up to her in the halls and say hello after you've talked in class a couple times. You will make a good impression if you do nice things, like holding a door for her to go through or tying her shoe if you notice it has come undone. Do not go out of your way to do these things all the time. She will think it is weird instead of sweet. Many guys prefer to cut to the chase, but if she is worth asking out, it is worth building a friendship. If you ask her out without getting to know her first, she might turn you down just because she doesn't know enough about you to say yes. Text or chat with her for long periods of time. Girls love it when this happens. After you've texted her for a while and you think she's good enough friends with you, try to ask her who she likes. Make sure she asks you too, otherwise it will most likely end up being a different guy. Also try to make it late—that's extra cute! Do you have common interests? Are you around the same age? If you are going to date this girl, make sure that she is someone with whom you actually want to spend a lot of time. It is easy to build up unrealistic fantasies in your head, but it isn't always easy to gauge whether you would truly be happy with someone. Try talking about what motivates her; by doing so, you will create a bond between you two. Ask her and some of your other friends if they would like to go somewhere such as the mall or movies. Eventually if you two are comfortable with each other you could ask her to hang out at your house with a group of people. A group of people will make it seem less awkward.  Don't ask her specifically to something and build it up. Instead, arrange something with a group of friends and say she is welcome to come along. That way, if she can't make it, no harm done and you can recover from the rejection without problems. When inviting her out, it has to be something fun that isn't a big deal for her to join in on. You want to avoid the awkward staring at your hands/feet mumbling about "what she is up to that weekend". If she is already dating someone, then that is her business, and you need to respect it. If she's obviously interested in someone else, then it might be worth your while to win her over—but do not get your hopes up. When you two start hanging out a lot, people will start talking and wondering if you two are dating or if you have a "thing." If people ask you about it, just say, "we like hanging out," or, "we have a lot of fun together." Never say, "we are just friends." This will give her the wrong impression. Ask her if she would like to hang out sometime, but don't make it sound like a date. As you spend more time with her, invite fewer and fewer people, so that eventually you can just say, "Want to hang out this weekend?" If she says no thanks, don't drop it yet. She is likely not comfortable enough with you, but she may come around if you keep talking to her. You could explain that it wouldn't be a date, just going to the movies as friends, or hanging out and going swimming.

Summary:
Get into conversations. Become friends with her. Text her. Make sure that the two of you are compatible. See if she wants to hang out in a group. Make sure she isn't already interested in or dating someone. Play it cool, but don't make her think that you aren't interested. Invite her to hang out one-on-one.