My favorite way to meet new people is through my existing set of friends. There are many benefits, the obvious one being that my friends tend to have great taste in people.
But I'm also at least a little bit awkward. Despite consciously thinking about asking thoughtful versions of default questions when I don't have a good starting point, I still get nervous when I don't know if what I'm saying will interest the person I'm meeting. While I don't think that friendship is transitive, starting off on topics that don't interest both parties can cause people to miss out on what could otherwise become a good conversation or even a lasting connection.
If you're introducing your friends to each other, try to suggest something they'd all enjoy discussing.
Sometimes, there's something specific and convenient to talk about:
- "Liz studies voice; she loves singing opera and operettas. You mentioned you saw Falstaff a few weeks ago?"
- "Both of you enjoy cooking. Liz, I know you spend most of your time in the kitchen with a Dutch oven, but have you tried pressure cooking yet? Karen made amazing pressure cooker oxtail last week."
- "You and Geoffrey are both passionate about open-source software. Geoffrey worked on providing software for MIT's computing systems via Debian packages and repos; I think you've submitted patches to some of the packages he's worked with."
Other times, there might not be something precise, but you can still find common ground:
- "I think you've both mentioned liking classical music."
- "You and Karen both studied computer science in college."
- "Geoffrey's been working out of coffee shops lately. I know you have a favorite coffee shop, but forget what it is."
If you can't think of something they have in common on the spot, mention something you find interesting about each of them.
Though you don't have to say something about everyone in the same breath - you want to leave spaces for the conversation to expand. If it looks like people are clicking, you might even get away with only introducing one person!
- "Liz and I traveled to Sweden earlier this year, and we stayed in a treehouse."
- "Karen started powerlifting a couple years ago."
- "Geoffrey and I are members of a church choir and sing a lot of Bach."
If you are meeting someone without the person who brought you, ask "How do you know people here?"
I love this question because I don't have to think too hard about what I'm going to say; I already know how I met my friends. Questions with obvious answers relieve some of the pressure around introducing yourself.
 Pun wasn't intended about coffee shops and common ground, but then I decided I liked it. Sorry not sorry.