I can start conversations with chicks easy at partys and other places, but there gets to be a point where I just run out of things to say and they don't seem to have anything to say to me either. What are some things I can do to keep the conversation going?

just talk about anything. assuming you have friends just talk about the same topic you talk about with your friends (except women).

to tell you the truth, it comes naturally, if you don't think too much about it and both of you are relaxed things will come naturally.

but if both of you think too much and are afraid of saying something you wouldn't like then both will fail.

I have to admit I have this kid of problems too, but then I think that why should I feel like that? she is just a girl after all.

Hard to advise with this and conversation really is one of the most natural of intuitions for humans. You really, really can talk about anything. Just be interesting and show interest. Practice and you'll get better :)