One's first public performance can be daunting in terms of the amount of anxiety involved. How should first time performers who have never been on stage (or performed in front of unknown people) deal with this? What are some good tips that seasoned performers use?
The best thing you can do is to know your stuff.
Practice it well beforehand, and know your material very well. This way you can get into the groove and stay there (and not be thinking about how sweaty your palms are, or how you're certain the folks in the back row can see your limbs trembling from fear) and then the next thing you know will be along the lines of "oh, I'm done, and lightning didn't strike me dead."
Public speaking is another type of performing in front of others that takes a lot less practice than performing a recital. With the same fears, panic and stress. Acting classes, or Toastmasters can alleviate some of the fears of being in front of crowds. Since most office workers will need to stand up in front of groups and give presentations (or at least argue your point), they are skills you will have to know anyway. With the confidence of a couple of talks or improv sessions, you should be able to recognize that you can do it and go through more difficult or challenging situations. This is part of why "boot camp" in the military is so stressful - you learn to feel the fear and do it anyway. Then, when you are in actual combat, you've already been scared to death, but you know you can do what has to be done.
Don't rush. If you have seen a lot of live performances you know that professionals don't run in, sit down and start playing immediately. Take your time; sit or stand comfortably and check the instrument and the music to make sure everything is ready.
Remember that the audience is not full of critics and music teachers. It's full of people who are there to enjoy the music. If you make a mistake, don't let on. Keep going. Believe it or not, most people won't even notice the mistake. If you have a memory lapse, don't go back but instead skip forward in the piece.
Best advice anyone gave me: If you're playing a recital, get the whole thing ready to play ONE MONTH before the actual performance date, and then keep practicing every day.
I agree with what Tangurena and Mark Lutton wrote, but would like to add some thoughts. I've been playing the piano since I was nine and had a lot of half-formal performances (so mostly in front of other music school pupils and their family) during the ten or eleven years that I've had music lessons.
I'm generally someone who likes being on stage, so I never really minded playing in front of other people.
One thing I will always tell people is that there's basically nothing that can go wrong. Yeah, you might forget the words or might mess up that part of the piece or forget where you are and start over or something. That might happen. But even if it does...
a) You won't die. Nobody will die. Nothing considerably bad will happen just because you didn't get that one little part right.
b) 99% of the time the people listening to you are already giving you credit for going up on a stage and performing for them. So, they will forgive. They already think what you're doing is cool and brave and they don't care if it's not perfect. Chances are you're already showing them something that they can't do but wish they could.
c) If you don't let it on too much or really have to start over again, people won't even notice when you mess up. I've had performances where I totally forgot the words and started a song over again from the start and people forgot that that happened by the end of the song. Either just be cool with it and say so ("Sorry, but I messed up. Have to start over, but this time I'll get it right") or - if you can - just keep on playing.
This sounds a bit pessimistic as I'm actually referring to how to deal with failure, but this is actually meant as encouragement. The best advice always is "Know your stuff". Practice. But if you're still nervous and unsure, understand that failure on stage is not the end of the world. It hardly ever actually is failure after all. If you can remember that, you're more likely to be calm and cool on stage and less likely to actually forget anything.