Usually you ask questions. @zenvelo‘s patter is one way to go, but you could follow along almost any line of thought. It has to do with the circumstances of your meeting.
Last night I was a a gathering of alumni for my college who live in my city. There was no one there I knew, so I was starting at zero with everyone.
Of course, the one thing we had in common was our college, and so you can always ask when you graduated. But inevitably, the next question is what are you doing now. How long have you been here? How did you get here? Etc.
I often feel a little unimaginative asking “what do you do,” but basically, that’s what I want to know. Work is fine, but I also am interested in other things you do. It’s the first question that is hardest, usually. The other person has to decide how invested they want to get. Am I going to be an interesting conversational partner? Is there some future for this conversation? Are we going to have fun? Are we going to make a professional connection? Are we going to make a social connection?
You never really know for sure what your agenda is, I think. For me, last night turned out to be a professional conversation and a social one. The first person I spoke to after the official greeter turned out to work where I work. Not only that, he turned out to work in a related department and he had in mind to come and give a talk for my audience. Who knew?
My wife ended up talking to someone who wanted to go to the dance workshop we attend. These are both pretty specific audiences or groups and there aren’t that many people who fall into these groups in the city, I don’t think and yet… this happens a lot, I find. Almost anywhere I go, if I’m open and outgoing, I find people who are related either through work or fun or neighborhood or through people we both know. It’s kind of scary, but it makes me think we are all much more closely connected than we know.
Anyway, my wife and I had dinner with my new colleague and his wife, who also turned out to have worked for a former employer of mine and on it goes. Connection after connection.