in need for some good advice

I have been going out to eat with this girl I met in class. We have fun when we go out but I havent closed on anything. I decided that I would enjoy dating her but am not really sure how to go about it. Should I let things progress naturally, I can tell that she is in to me, but I want to start something more serious so I dont think it is a good idea to push, but I also dont want to come off as a p*ssy. Does anybody have any ideas on making the transition to becoming more intimate, and how can I get better at closing?
thanks for any input