Does a girl like you when she tries to avoid you and smile when you say hi to her and look at you often but when you talk to her on instant messenger she's very quiet and doesn't say much at all?

Since she's smiling at you it's a good indication she is interested, but she could just be shy. Instead of side-stepping each other why don't you just walk up to her and ask her out on a date. She could be wondering why you pay attention to her, talk to her on IM, but never ask her out. Try asking this girl out! Good luck Marcy