I think the way most people use Facebook for networking is to stay in touch with people they've met incidentally in person. It's a way of sustaining or developing an otherwise tenuous in-person contact, but the vast majority of people don't friend people they've never met.

I Facebook friend people I've met just once at parties, conferences, while traveling, etc.—so that I get to know a little more about their lives and so that when I see them again at similar events, I remember them. And maybe we'll have things to talk about. I can say, "Hey, your brother just had a kid, right?" or "Congrats on finishing law school" instead of, "Didn't we meet at that one party that one time?"

Definitely wouldn't message someone I've never met. Don't accept friend requests from 'em, either.