How can I help my child learn?
Positive encouragement and reassurance are the most important things you can offer. Help them to get themselves organised, to get into a routine of practising, but also let them work independently. This includes making mistakes, which are an inevitable part of acquiring new skills, so give them the time and space to try and figure things out for themselves.
It can be very helpful if you discuss what they're doing from time to time, though. For example, you could ask them to show you what is particularly important or difficult in a piece they're learning and how they should tackle it, to help them remember what's we've talked about in lessons.
Let them feel welcome to play their instrument - don't shut them away in the farthest room or the garden shed, and don't complain about the noise (unless it's at a ridiculous time of day!) If they start to feel self-concious about disturbing other people, they won't be able to concentrate properly on learning and improving.
Any learner, of any age, will have days when nothing seems to go right, and gentle sympathy is all that can be offered. On the other hand, when you can hear progress and improvement, be sure to say so.
Finally, if you feel there's a problem that you can't solve, or you need more advice, then feel free to ask me. Email is best, because then I can check back on records of what we've done in past lessons and make sure I explain things correctly.