People always ask me about how to handle nerves and anxiety about performing. Specifically, they want to know how to prevent memory slips and other mishaps during performances.
My answer is in two parts: what you do before the performance (your preparation) and what you do during the performance.
Before your performance, when you are learning, polishing and perfecting your pieces, you simply must get to know the music in the very core of your being. How is this done? By really hearing it, hearing every relationship, every harmony, every contour of the melody, every architectural structure. I do this in many ways. One important step is to first learn to play an outline of the piece so you can clearly hear the basic structure or "architecture" of the piece, without all the distracting details (see my earlier post on outlining). Another method is to play each voice separately (even non-polyphonic pieces contain as least some passages with distinct inner melodic lines), and anything that is a basically a chord in blocked form (such as an arpeggiated left hand part). However, this is not the same as hands separately. If I play one voice separately I play it with both hands (the other hand just doubling it at the octave) so that I am using both halves of my brain. I also play with eyes closed so that I become totally independent of needing the visual cues of either the page or the keys themselves. And most important, I transpose every piece to all keys, at first using the written page as necessary, but later totally by ear/memory. Transposing ensures that you hear the relationships; since you are no longer playing on the actual notes but a different set of notes, the only thing you CAN hear is the relationship. In performance, if you have a brief stumble or even memory lapse, you will be able to quickly recover and go on because you know the piece so well. It is a long process, but when you can do this, then you can truly say you "know" the piece.
What you do during performance is a tricky one. The key is to set your ego aside and just listen. Listen as openly and as intently as you would like your audience to be listening. We must train our minds to be quiet and not to chatter. You do not want to be thinking about the notes, about whether the audience is responding well, about the next piece you will play or the difficult passage coming up, or about where you will go to dinner after the performance. The mind wants to fill itself with these thoughts but when you realize you are thinking, you must keep coming back to listening. In this way it is just like meditation. Thinking about "the notes" is the most deadly. As soon as you think about what notes come next, you will miss them. This is because you have spent your hundreds or thousands of hours getting your mind and body "wired" to play the piece from some very deep part of your being. That is why when you play well you have the sensation of just watching it all happen. If you start thinking about it with your conscious mind, you get in the way of the "self" that really knows the piece, and you will stumble. (You can find plenty of references to this concept in books such as "The Inner Game of Tennis" and others, which deal with the same idea as it pertains to competitive sports.)
When you really listen, you will find yourself responding differently to what you hear each time you play. Thus, I will make slight differences in dynamics or nuances of timing each time I play, because I am free to respond to what I hear. This is what makes live performance exciting, for both the audience and the performer.
You have to try to take yourself and your ego out of it and just present the music in the most straightforward, yet beautiful, way to the audience. You don't have to "try" to make the music beautiful -- it already IS beautiful. Just get out of your own way. Even though many of us who perform do have strong egos, at the moment of performing we must set them aside so the music, not our egos, can take center stage.
If you have a stumble or small memory lapse, you rely on your preparation to get you through it without stopping, or worse yet, trying to correct or repeat the passage. It is difficult not to keep thinking about what just happened, but again, it's coming back to open listening that is the only solution.
If you practice these methods you will get better at them, naturally, and you will learn to trust yourself. When I see people who bring their written music to the performance and spend their last few minutes before going on stage pouring over their music, I know they don't trust themselves. That kind of last minute "cramming" just undermines your confidence.
When I sit down to the piano at the very beginning of a concert, my favorite thing to do is this: I look out over the beautiful 9 feet of piano stretched before me and feel gratitude that I get to play such a glorious instrument. I silently dedicate the concert I am about to play to my teacher, Joseph Prostakoff, who has been gone for almost 32 years, but who I think of daily. Had I not been lucky enough to find him I would have given up the piano. Then I just take a few breaths and calm my mind, yet at the same time I feel excited to play the music. And then, jump in. Remember, the experience can and should be fun. If you truly love the music you are playing, you can find the fun in it no matter what happens.