How was a child's life in the Middle ages?

Children did not get much time to grow up. Peasant children were usually working at age six. Children who were intended for trades, crafts, the Church, or knighthood usually started apprenticing or going to school at age seven or so, and that was what they did for about the next fourteen years.
Children were very exposed to medical problems, especially childhood diseases, so something like half of them died before they were five. At some times, the life expectancy at birth was not much over twenty because of this, but if you could get to age five, then you were quite likely to live past into your fifties or longer.
A good deal more information can be found at the related question below.