Practice deep breathing on a daily basis, so that it's something you can automatically turn to during a performance when you get anxious.
Practice your performance ahead of time in front of a few close friends and/or family members and encourage feedback or constructive criticism. You can depend on your close friends and family to tell you their honest opinion, and this would enable you to alter your performance accordingly. If you are comfortable with performing in front of the people closest to you, then you should be able to perform in front of a multitude of people with less problems.
The more you practice your performance, the more you become confident that you can deliver. The objective is to internalize your performance so that you would be able to perform in the midst of distractions. One night of rehearsal isn't enough time to determine if you have your performance memorized. It is best to prepare well in advance to ensure that you know the material you are performing.
Focus on the positive aspects of your performance, instead of the what-ifs, like "what if I miss that note?" -- take the focus off of yourself so you can concentrate on the performance itself. Focus on how beautifully you're going to express your emotions.
As you breathe during the performance, go with the flow and accept the anxious feelings. Give yourself permission to feel the anxiety instead of fighting it. Then you can use that energy to fuel your performance and start to think of it as excitement instead of anxiety.