When your child first begins lessons, for the first two or three weeks, 15 minutes per day is good practice. You can break the 15 minutes up into three or more sessions if you wish. The child should go over everything we talked about in lesson. I write the list in a composition book, so you as parent can see what we did and help your child review it. If a child finishes the assignment before the time is up, he or she can go back over the lesson from the beginning, or review pieces done in previous lessons. Very soon I will want your child to be practicing 30 minutes per day, or as many minutes each day as the weekly lesson is long.
The purpose of piano practice is never merely to be able to play the pieces. If that were the purpose, you could go over the assignment with your child only on the day before the lesson. Instead, the purpose of practice is to gain muscles! That's right. Your child may complain that he or she can't do what I ask at first. Indeed, it is impossible at first, as is any new project in strength training.
The purpose of piano practice is three-fold: 1) to build muscles in the fingers, arms, and torso; 2) to build habit patterns in the brain for the many kinds of touch and movement required; and 3) to train the ear to listen and recognize specific sounds and patterns of sound. Practice for the required minutes on five days each week will grow these results.
Parents can help and optimize the learning. We teachers call the ideal finger shape "curved fingers." I've even called it "curled fingers" or "bubble hand" in order to get the children to build the muscles I want. The muscles and tendons connecting the final joint in each finger must grow strong in order for the fingers to move quickly, precisely, and be able to produce beautiful sound nuances. You will help your child immensely if you will remind him or her to curl the fingers.
The other thing you can help with is the alphabet. Your child needs to know the alphabet, A through G, both forward and backward. Then a few weeks later, he or she needs to be able to name the keys on the piano and then, later yet, to name the notes as they appear on the music staff. Don't worry about not knowing them yourself, just ask for him or her to show you a "D" for instance, or an "F." If your child is hesitant in showing you this, perhaps I haven't taught it yet, and that's okay. So, ask him to come and offer to show you as soon as he learns it, and quiz him about it several times after that in order to settle it in his mind.
For children who have advanced beyond merely knowing the notes into intermediate skill level, I have only two basic tips: 1) Finger exercises at the piano are important to build and maintain the muscles that produce beautiful and precise sound. When on vacation, if all you have time for is a few finger exercises each day, this will make your re-entry into practice much less frustrating. 2) Once each week, devote your practice time, after finger exercises, to something really difficult, way out beyond your current performance level. I won''t assign it or ask to listen to your performance, but if you will spend this time honestly trying to figure it out, there will appear a big difference in your skill and confidence level, noticeable the very next day when you return to your assignment.
I have two mileposts as the children advance. When they begin studying out of teaching curricula made by the classical masters, it's a big thing. And when they begin playing out of a church hymnal, that's another big thing. Of course, I'm working toward the vision of a determination within each child to surpass the milepost and master, with improvisation, each of these bodies of literature.
So practice, practice, practice! For at least as many minutes each day as your lesson is long!