Anyone below Bar/Bat Mitzva need not fast. However, they should not eat excessively.
From the age of nine (or ten if the child has a weak constitution), children are trained to fast at night and for several hours during the day, as per the child's abilities. A child below that age should not skip any meals.
All the other prohibitions of Yom Kippur (i.e. leather footwear, bathing and anointing) are applicable to children of all ages. Therefore, an adult may not encourage or assist a child in any of these activities, or make it accessible to them.
If a child performs any of these activities of his own volition, he or she may be left alone if younger than nine. If older than nine, the father is obligated to correct his child's behavior, and must also prevent the child from eating during the hours when he or she should be fasting.
