Tageted towards high school and college shy guys who want to know how to flirt with cute girls.
Crack a joke. Girls know when you're trying to talk to them. Crack a joke and show that you have a sense of humor. It doesn't have to make her laugh, but getting a little smile is all you need to get started.
Ask her for help. Girls love being asked for advice. You could ask for help choosing a new shirt, help with homework, or help getting "the girl you like" to like you. Use all of the romantic advice she gives you on her!
When she's in a group. When a girl is in a group it can be challenging to talk to her. Sometimes it's easier to walk up to the group if you know someone else. Get to know one of the girls she hangs out with. It will be easier to talk to that girl first since you don't like her. Then use her to get into the group and eventually talk to the girl you like.
Don't give her all of your attention. Girls (especially cute girls) are used to having guys pay lots of attention to them. Talk to her, but don't give her too many compliments. Talk to her friends and tease her a little. It will make you interesting to her.