The absolute, number-one, most important thing to remember when playing live music in front of an audience is this:
IF YOU'RE NOT HAVING FUN, THE AUDIENCE ISN'T HAVING FUN
It doesn't matter if you are a serious folk act, or a surf-rock band, if the audience senses you are uncomfortable on stage they will become uncomfortable themselves and only applaud because they are being polite. They might have paid a lot of money to see your act in a club, or they might have paid nothing at all, because it's an open mic night at a local coffeehouse, but a live performance is a fluid situation and no one likes to see an act uncomfortable on stage. Which leads us to our next bit of advice:
DO WHATEVER IT TAKES TO BECOME COMFORTABLE ON STAGE
Bring your favorite throw rug from home to stand on, make friends with the sound guy, draw an imaginary circle three feet around you and declare that it is "your space" and then proceed to make it yours by behaving like a mad person (as long as it includes our first tip above). Basically, just do your thing and pretend like the white hot spotlight isn't there. Every audience is dying to be turned on and it's up to you to do it. So, how do you turn them on:
REHEARSE, REHEARSE, REHEARSE....THEN FORGET ABOUT REHEARSAL
Being well-rehearsed is of paramount importance. It's like preparing for the big test in school. You're ready to go if you're well rehearsed, but once you get on stage things won't go like they did in rehearsal. Be prepared for this as well. Going from the rehearsal space to the stage is like entering a new frontier. It is at this point you must heed the advice that Yoda gave Luke Skywalker and "unlearn what you have learned." Which leads us to our final tip:
IF YOU MAKE A MISTAKE ONSTAGE, KEEP GOING LIKE IT DIDN'T HAPPEN
The true designation of a professional isn't the money they make, it's the ability to cover up a mistake on stage. Most times the audience will not even recognize that it happened...if you just keep going like it didn't happen. There are many ways to do this.
If a singer forgets the verse, revert to the chorus, regain your bearings and come back to the verse.
If a player misses a note, just play the wrong note again, so it feels like a pattern.
If none of these tricks work, just smile and laugh and keep going, as if to say "yeah, I just messed up, but it doesn't matter, because I'm having the time of my life up here." The audience will smile and laugh too, which means they are still with you.
Which, of course, brings us full circle back to a slight variation of tip number one:
IF YOU'RE NOT HAVING FUN, WHY ARE YOU DOING IT?
You shouldn't want to play music on stage just to be rich and famous. You should do it because it is in your blood and you truly enjoy doing it. If being rich is what you want, open a fast-food chain with your rich Uncle or get into investment banking. If being famous for fifteen minutes is what you want date Paris Hilton or be a YouTube troll until something hits, but for God's sake don't start a band. If you're a singer or a musician, know that all you can do is get better at your craft, no matter how talented you are. And have fun doing it.