Anxious about talking to people

I'm going to a couple of group meetings in about a week. I want to make friends, but there's a problem, I'm socially awkward. I have a hard time starting conversations and possibly saying the wrong thing and carrying conversations since I often don't know what to talk about and end up just saying nothing for a long period. I'm worried that I might not be that well liked at either of the groups since there will probably be more interesting people there worth talking to, and will continue feeling lonely for the rest of my life, especially with how the past year or so has been treating me. How do I overcome social awkwardness and bond with the people around me?