There are a lot of suggestions, but I'll add some as an introvert myself. I hope I'm not repeating.
I HATE HATE HATE large crowds. I seriously hyperventilate when thinking about going in for coffee hour, all right? Get the picture?
However, I guess that I'm a bit different in that if a person is actually interested in every day conversation and isn't faking, I open up quite quickly. I actually hate politics talk because to me, it is utter fakery. And as someone who studied and spent years debating just about everyone who lived in my dorm, I hate
talking about politics. Usually people repeat the same stuff. You guys think you have amazing insights that I've never heard before? You don't.
Really. I promise.
If it's about a specific topic that's current in the news, it's fine. But if I hear another "What is happening to our country" discussion, which usually precedes a long monologue, my eyes absolutely glaze over and I look for the exits.
I think introducing him to some people who have stuff in common is a good idea. Maybe even playing sports with one of your relatives (doubles tennis, bowling) or video games can help create bonds. Even going to a movie! It's weird but sometimes people feel more relaxed afterward, being in other people's spaces for a while.
I think the one-on-one aspect is key. After spending time with my future godparents outside of a church environment, it's been a bit easier to just chill out at church and sit back during coffee hour. Sometimes we get into a big discussion with a table of 10 people, sometimes we talk to 1 or 2 people, sometimes it's just "Hi"s. Whatever. I still get a little nervous but it isn't TOO bad.
Question to introverts who don't like to talk about "personal" topics: What the heck do I talk to you about? Of course I'm not asking about salary or your love life, but I'll usually ask where the person lives, how long they've been in the area, what do they do. If I feel like they don't want to answer, I'll change the subject quickly.
But I am really interested in other people, and I find it such a hurdle to overcome, to talk to people who just don't want to say anything. I don't watch sports and I try not to bring up politics because the chances that I will offend whoever I'm talking to are quite high.