meetup.com abunds with events where you can meet people. You can start with the boardgames events, those are usually small-sized and no need to make big efforts to socialize, playing the game does that for you. Toastmasters are also great events, very supportive.
Obviously at some point you will need to get help with your anxiety, but here’s how I dealt with mine:
I used to be scared of going out to events, meet people, even just bring my laptop to the nearest Starbucks and work there. So I went by this method: I’d ask myself what is the closest thing to what I am afraid of–socializing with people–that I could manage to do.
At first it was just stepping out of my room and walk around for 10 min. So I’d do that. Not telling myself “I’ll go to the gym and get a membership” or even “I’ll strike a conversation with someone,” just “I’ll walk on the street, look at the pavement and do that for 10 min.”
Eventually I got comfortable to that. So I asked myself again, “what’s the closest thing to socializing that I can do.” That time I took a walk, and made eye contact with people. When they’d notice me I’d smile. Nothing more, no words exchanged, just a look. Again, at first it wasn’t comfortable but that was something I could still do. Maybe some days I couldn’t, then I’d just go back to look at the pavement. But slowly I managed to work through this eye contact thing.
Then came sitting at a Starbucks, doing my work. Then, small talk with the barista. After that, giving a compliment to a stranger on the street. Then, making small talk with three people on the streets. Every day I’d set myself a goal that seemed achievable yet just next to the edge of my comfort zone. Eventually I managed to bring myself to a point where I’d strike conversations with girls on the streets and get their numbers.
So again, the point is to set yourself achievable goals, make baby steps. At any failure, take a small step back. Even if you just start by looking at people by the window, that’s a start. Progress slow but steady, and eventually you’ll start getting more active.