I think the best solution for some folks is to simply force yourself into the situation over and over, like going to a meetup and making yourself talk to everyone. Eventually, your brain will get the idea: okay, I can deal with meeting and talking to new people.
Here's my tip: learn how to ask great questions when you meet people. It takes the spotlight off of you and let's them "do the work". I can have entire conversations where I say very little if I'm feeling anxious at the moment.