Find a common interest you can talk about. If you can't, the friendship will probably never happen. We can't just do small talk for hours.
Be patient, if they are not opening up immediately, it's not because they don't like you.
Take the lead in trying to set up get-togethers, at least for a while. It's hard to reach out to someone to arrange something when you have social anxiety.
Do arrange one on one meetings over group meetings. We suck at group conversations. With everyone talking over each other we can't get a word in and feel ignored. Some socially anxious people avoid these things altogether.
Lead the conversation, give us something to talk about, open new topics and shit. If you find the right topic (see point 1) you can get great conversations.
However, "lead the conversation" doesn't mean talk over the person and never let him get a word in. Don't be overbearing.
Don't do stuff like joking "roasts", some people like it but someone with social anxiety will likely assume you legitimately hate them.