Occasionally I have the opportunity to serve as a judge or adjudicator at festivals and competitions. It's a great learning experience for me, as well, as I'm often looking for indicators of a musician's preparation beyond the music.
Here's what I mean.
Many times a musician is playing very well, but not performing well at all. The music may be really great, but performing means going beyond the music and presenting yourself well in all areas.
In a formal or school-type setting, like a recital, here are a few factors to consider:
1. Appropriate dress. You wouldn't show up to a rock concert in a tux, so why would you show up to a recital in a t-shirt? If there are any questions as to what is appropriate dress, ask the teacher or conductor - or your bandmates - or go online for some pictures or guidelines for the type of event you're playing at.
2. Speak clearly. Many a good performance has been ruined by sloppy language before the music starts. Again, ask your teacher for help or find some information online. A good place is to simply tell the audience clearly who you are and what you will be performing. If you don't know what to say, just smile and play your piece. Let your music speak for you.
3. Stay in 'character.' Keep your composure! Keep a pleasant expression on your face, don't react to mistakes, and - unless it's part of your performance - don't let the audience affect you. Things are bound to happen - someone will sneeze, a baby will cry, you'll drop a stick, or whatever. Don't get frustrated, just keep playing. If you have to stop (to pick up the stick!), just start back where you stopped and move forward as if nothing happened. If you don't make a big deal of it, chances are, neither will your audience.
4. Don't apologize. Before, during and after the performance, keep your game face on. Don't say things like, "I really didn't practice that much," or, "I'm not ready yet, so this isn't going to be that good," or anything before you play. Even if you know it's going to be terrible, refer to number 2 above.
During the performance, no matter how many mistakes you make, keep playing. Do not say, "Sorry," or, "Let me start over." Just keep going. Don't acknowledge your mistakes. If the absolute worst happens and you just can't finish, simply smile at your audience, bow or say, "Thank you," then walk off the stage. When the applause happens, acknowledge it with a nod, or bow and smile.
5. Accept compliments. Even when you feel like you've had the worst performance of your life, someone is bound to tell you how great you did. You'll want to say something like, "What?! Didn't you hear that? I was horrible!" But don't! Just say, "Thank you," and leave it at that.
6. Be prepared. Maybe the best way to build confidence is to be very well prepared. If you've practiced and polished your music until it shines, and you know you can play it very well, you'll have no trouble feeling good about the performance, and you'll have no reason to be awkward or ungracious.
7. Stay engaged. If you're not playing solo, make sure to support the other performer(s). Never give any impression that you're bored, tired or distracted in any way - even if you have to rest for 168 measures. If there is a solo going on, watch the soloist. If someone is singing, look in their direction. Try to let the audience and your fellow performers know that you are supporting them in any way that you can, even if you're not playing.
8. Don't distract. Even if it's a rock concert, there's a time to play and a time to keep quiet. Especially in between songs, don't practice or "noodle" on your instrument. Start together as a group, and end together as a group. Let all of the sounds you make be part of the music, and on purpose. You may think that everybody knows that you're making sure your snare drum is working, but all the audience hears is unnecessary noise.
Next time you go to a live concert, pay attention to what the performers do aside from playing music. You'll start to notice pretty quickly that some things make the performance better, and other things make it much worse.
With a little effort, you can not only play great music, but have a great performance, as well.