It is actually very simple. Just say hi, and basically do what you would do to make a friend. Then get to know them, and if you think they are the right person, Wait until the right moment and ask them out! It is easier if nobody is around and you are doing it alone with just you and her.
The hardest thing is walking up to them, and opening your mouth. The best way to do that, however, is indirectly. In other words, don't just walk up to her, and say, "Hi, my name is--." No, you don't want to do that. Find another way to walk up to her. If you twp have a mutual friend, have them introduce them to you. Or, you could say something like, "Hey, I really like that jacket!" "Awww, thanks!" "Where did you get it? I have a cousin who would love to have that!" Girls LOVE it when you notice things like their outfit, hair, etc. You could also sit next to her at lunch. As far as things to talk about, talk about things SHE likes. And the #1 rule on how to talk to girls is to listen more than you talk. Let her be the one to talk.
Ya know....this question might get (and has gotten) a lot of quick answers but this is a real question. The first time around, just the thought of chatting with a young lady would cause your knees to shake. It's not as easy as some might make it out. But here's the thing.... take a chance. Be confident. Keep it simple. Keep it casual. Doesn't have to be quantum physics or the meaning of life - just a casual conversation. Once you calm down and relax, you'll be yourself and that will be recognized for what it is. There's always the first time. And looking back, that's the most fun of all. Go for it and enjoy.