Don't know much about how to do the chit chat, but when you ask for the date, here's what worked for my dad and uncle perfectly: I was thinking I would go to the ____, and wanted to know if you would like to go with me, if you don't have other plans? There could be three situations. First, she wants to go and is free. Ok. Second, say she definitely doesn't want to go: The last phrase gives her a graceful way out if she doesn't want to go with you. It also saves face for you, and she is spared having to make you feel too bad. Finally, say she might possibly want to go: You've removed the pressure on her to immediately answer with an unqualified Yes or No, so she is relaxed and can think about it for a moment. You have again saved face if she does say no, and you don't appear pathetic. Since you don't look pathetic and she hasn't flatly said no, you might succeed another time. A variation of the method is to say, my friends and I were planning to go, etc.
Introduce yourself to her, or just start up a conversation. Let her get to know you a little and then ask her if she would like to hang out sometime. Maybe you already are talking a lot. So, now is a good time to ask. Make it sound casual if you think this is what the girl would want. It's hard for her to believe she doesn't like you, if she doesn't know you. After some conversation or casual contact you may decide you don't want to go out on dates with her, just be friends. It's always hard to be told no, but you will never be told yes if you don't ask in the first place.