So, this conversation is happening in the comments, and it's a pretty interesting question, so maybe we can all work together to make a How to Make Friends post?
My local board game shop is SUPER friendly. I'm very lucky. Every single person here is friends with everyone else because we all invite people into games and ask to join games at will. I didn't make it like that - in fact, I have pretty bad anxiety.
But somebody DID make it that way! A handful of friendly people started it. The shop owners were definitely the ones who fostered the community the most, but the patrons are the reason it worked.
It turns out that if you have just a few people who are friends with each other and feel secure enough not to feel to anxious, they can make it so everyone feels welcome. We have a guy here who is The Friendly One, and every time we notice a new person, we walk him over and he introduces himself, asks how they're doing, asks what kinds of games they like, etc. And the mere fact that one person is like that kind of gives the rest of us permission, too, so it's not as awkward.
We also are all super down to spectate, just walk up to a random table and say "do you mind if I watch?" If the guys playing say yes, you watch for a bit, and you might end up having a conversation with one and Boom, you have Made a Friend. Usually at least one person at the table will answer questions about the game, and talk about how it's going. If it doesn't click, though, and you just feel awkward, you can move on to the next table.
So, that's my big advice:
1) Once you have enough friends to feel comfortable and secure, remember that you can be the one who makes your community better.
2) If you have an excuse to talk to people, even if it's a dumb thing like watching a board game, you might accidentally end up making friends.
It took me a long time to learn this!
Anyone else have some additions?