What to expect
Parents of young students should observe lessons and be hands-on at home, helping their child practise (this means sitting down with their child, going through their notebook and practising each task, making sure that the child understands each task and achieves it).
Parents of older students who are more independent still play an important role in acting as a coach, offering encouragement and pushing their child to work hard and be disciplined about practice.
Students should have a positive attitude, a willingness to give everything a go and to make mistakes, and make a commitment to regular practice.
Parents and students should understand that there will be peaks and troughs in the motivation to learn and practise piano, and it is important make a decision to work hard and practise regardless of how one feels day-to-day.
Students must have a decent digital piano (88 keys, in a cabinet, with 3 pedals—like the Roland F140, which I recommend) or a well-maintained, in-tune acoustic piano.
Toy pianos or smaller-length keyboards will not suffice; you would be better off saving the money you would have spent on lessons to acquire a decent instrument first.