I'm pretty new to this game, a bit of a late comer. I met this girl at university, and she seems to enjoy spending time with me. She might want to be just friends, but I'm hoping she wants more.

What can I do during this gathering to show interest in her and move things along?

UPDATE: Utter failure. There were at least 30 people there, she was hanging out with a group of them, while I sat on the couch with the people I know. I didn't feel comfortable following her around, or even approaching her and talking. She seemed into other guys. Oh well.