The most important organ of your body in piano practicing is your brain. Whenever you practice, you actually create neural pathways in the brain. With each repetition, the pathway is strengthened. A strengthened pathway is one in which the neurons move faster along the nerve to the next nerve. At a certain point, whatever you have practiced will be produced without you having to give much thought to it. An illustration of this is walking. When you walk, you are in auto-mode. You don't have to think about:
- shifting your weight from one leg to the next
- moving your leg forward
- coordinating the weight transfer with foot movement
All these things happen without conscious thought.
Practicing accurately to construct a correct neural pathway is crucial. If your allow mistakes in your practice, then that is what will come out when you are in auto-mode. Perhaps you have experienced trying to correct or change some notes or some phrasing after you have learned it one way. You think you have corrected it. But when you are under stress with performing in public or at a piano lesson, the old way resurfaces. This occurs because the new way is not as secure and established in your brain as the old way. It takes a lot of correct and accurate playings to make the new way of playing stronger than the old.
Once you have learned a piece or a few measures, you can mentally practice. That means you can imagine the feeling of your muscles, fingers, arms, hands, wrists, elbow, etc while hearing the sounds in your head. If you do this, you will find that your memorization of the piece becomes more secure. This is a great way to practice when you don't have access to a piano.