Ignorance can be bliss. Very young piano students really have no idea that playing in piano recitals can be stressful. Often, they are chomping at the bit to get up on stage and put on a show!  On the other hand, pre-teen and teen students, who are becoming more self-aware, can suddenly realize that there is an audience listening to them and this can be a very startling and scary revelation.   For these students, learning to deal with nervousness and butterflies becomes as important as being well-prepared.  Not only this, but piano performance requires the ability to adapt within seconds of your hands touching the keys. Unlike almost all other instruments, amateur pianists and piano students can't bring their own piano with them to their performances.  For pianists, the luxury of playing on your own instrument is really confined to very famous concert pianists who can and do ship their pianos ahead of time to their performance venues.  Even when concert pianists can't bring their own instruments, they will take the time to try out and even select a local piano to perform on.  I know that at least a few of my students have experienced and/or learned these truths. Yes, it does take much more than simply practising on a regular basis and preparing your pieces well to have a successful performance.  
Over the years, I have experienced all of these things and more when performing, the most troubling being the shaking of my fingers.  This phenomena set in when I performed as a mature adult.  I have been bewildered by it too as I have often found that no amount of preparation or self-talk can dispel or prevent it from happening.  The worst part about it is that performing difficult technical passages successfully, that you have mastered during practice, becomes almost impossible to do with shaking fingers.  Some might decide not to perform at all under such circumstances and give up entirely.  For me, rather than running away, I became more enlightened and I discovered the one thing that would stop my shaking fingers:  performing much more frequently.  I came to the inescapable conclusion that to become good at performance, a pianist needs to practise performance with the same diligence that is used to prepare the piece to be performed.  It is the best strategy that I know to ensure a successful performance.  A handful of performances each year through participation in recitals, exams, and competitions are not enough to become a good performer.  Specifically, I think that performance should be practised on a weekly basis at a minimum.  Today, when I have a piece that is well-prepared and thoroughly memorized but I am still hesitant to perform it, it is often because I have not been practising performance, or not been practising performance enough.   

Parents, family, friends, and even a refrigerator repairman can assist in creating a performance-like environment where a pianist can practise performing.   As parents, one significant way in which you can support your children in their music studies is to have them play for you.  For best results, plan to do so weekly outside of practise time, give them your undivided attention, and become their biggest fans with all of your generous praise and positive comments.  Students can ask to perform for other family members and friends too.  When there is a visitor in the house, this is also a good opportunity for a student to practise performing.  I have often played when a repairman has come to my home while he or she is fixing something.   In every case, the repairman has been delighted by the unexpected treat of a live performance even when I am working through some of my performance issues. Recording yourself is also an effective way to practise performance with the added benefit that you can assess yourself after the fact. Saving the recordings also allows you to hear how you have improved from week to week.  If a student walks by a piano, they should play it if it is permissible.  There are many places where you can find a piano.  This could be your own church, someone's home, a school, or a hotel lobby when you are on vacation.

Music is a performing art.  It is an art that does not really exist without a performer, and then, for only the moments of the actual performance unless the performance is recorded.  Learning how to perform is an essential part of any student's musical education and an on-going effort on the part of most pianists.