Here's how first time meets should probably go: eye contact, firm handshake, exchange of names, friendly smile, further conversation optional, end of story. It's really not that hard, though it can be awkward and nerve-wracking; but for some reason some people seem to not do one or more of these things.
Let's go through it one at a time, shall we?
1. Eye Contact
I'm surprised at how many people simply don't make eye contact. Personally, I find it somewhat rude when people don't look me in the eye. I know we're both nervous, please just do it.
2. Firm Handshake
Please no dead fish. Most men give me a firm handsake, but for some reason a lot of women don't think they need to. I think a nice, steady handshake shows that you care (whether it's business or casual) and that I mean business (when it's a business setting).
