I played guitar for someone the other night while she sang. It wasn't exactly the first time she's sung in public, but it isn't something she does regularly, so she was a bit nervous. I told her to get over it. After a song or two, she relaxed and everything was just fine. It got me thinking though about the first time I performed in public. I was in the high school musical. I didn't have a major role, but I had a few lines and had to sing a song or two. I just about puked before going on stage.
If you ever take a public speaking course, the first thing they will tell you is that most people fear public speaking more than they fear death. Personally, I think that's a line of B.S. someone made up to sell more public speaking courses, but the underlying theme isn't lost on me. Getting up in front of a group of people who are all looking at you and waiting for you to do something can be nerve wracking. Nobody really wants to be judged. The thing to realize is that we're often our own worst critics. Most audiences aren't going to notice minor mistakes anyway, and are pretty forgiving if they do.
The important thing is to give it a try.