In order to "chat up" a girl, you need to learn about her - this is also good because it shows you are interested.
(This also works when talking to guys)
During the conversation, ask open-ended questions - questions that she will have to give longer answers instead of yes/no answers - and listen to what she says. People love talking about themselves! This will help you to learn about her tastes, and will help you have a good conversation at the same time.
Some example open-ended questions:
Chat with our AI personalities
I am a girl so I will tell you! Try to be funny, but not too clownish, and kind, and understanding if she says something.
If shes preppy, talk about her. any other girls, you talk random. not random random but be funny (unless shes goth) if shes got, your screwed!