There is an interesting discussion on this topic on the ABRSM forum. You can find it here: ABRSM Forum thread on Performance Anxiety
Whole books have been written on this topic. An especially good one, packed with helpful advice on all aspects of becoming a musician, is Stewart Gordon’s Mastering the Art of Performance. The contributors to the ABRSM thread have made many valuable and helpful observations but they, like Stewart Gordon, seem to be overcomplicating. The main things are: correct choice of material, thorough preparation, and a track record of success.
We all know how it feels when the mind goes on strike, the fingers seize up, and a piece that you played 20 times flawlessly the day before falls completely apart. And we have all felt (whether it is true or not) that as adults we are unfairly judged compared to children with similar experience.
But if you don’t feel nervous or anxious before a performance then there is something wrong with you! And if you do feel anxious then you are in good company. Remember that even world class performers like Rubinstein and Horowitz also suffered badly before every performance. We do not want to get rid of that nervousness. What we need to do is develop the confidence to play well despite the nerves. In fact to use the extra excitement to enhance the performance.
To perform well you need to:
1. Believe in the music you are playing
2. Believe in your particular interpretation
3. Be fully prepared technically. So well that you can play your pieces on auto-pilot
4. Have the confidence that you can deliver before an audience
Numbers 1 to 3 are easy. Choose the right pieces, pieces that are totally in accord with your own feelings and ideas about music, think them through, make sure you have something to say through the music, and that you know how to project it, then practice like a demon.
But where does number 4 come from? Success breeds success. Once you have managed to hold one performance together, with racing pulse, shaking hands, and fluttering butterflies in the tummy, then the next one is easier, and the one after that is easier still.
The biggest mistake that novice performers make is to play material that is too difficult.
Picking pieces close to the limits of your ability is a recipe for disaster. Just because you can breeze through them at home does not mean you’ll manage them on the stage.
So start with something that is well within your capacity. Something that is so easy for you that you just know with complete certainty that you will play it well enough no matter how stressed you feel. If you are a diploma-level pianist then present a piece from the ABRSM Grade 5 syllabus. A lot of pieces at that level are every bit as enjoyable to listen to as the virtuoso material that we hear from the Kissins and Hamelins of the world. For example, If you can rattle off Liszt and Chopin etudes at home, then consider presenting a couple of tuneful studies by Bertini. Or if you can manage Beethoven’s “Waldstein” in the privacy of home, you might look at performing a Sonatina by Clementi.
And as you become confident (though probably no less nervous or anxious) and rack up several successful performances you can gradually increase the difficulty level.