The young boy is ordered to fast when he reaches the age of 7 is if he is physically capable of bearing it. (Some Muslim scholars that he should be physically reprimanded if he does not fast by the age of 10, which is the same rule that is applied to prayer; refer to Al Mughni 3/90). The boy will get a reward for fasting and his parents will get a reward for teaching him well and guiding him to that which is good. Al Rubayyi’ bint Mu’awwadh (may Allaah be pleased with her) said about fasting ‘Aashouraa’ at the time when it was mandatory to fast it and not voluntary: we used to make our young boys fast, and we made them a toy made out of wool. If one of the boys cried [wanting] food, we would give him [the toy to distract him] until it was time to break the fast." (Al Bukhari Fath # 1960). (Ashouraa is the tenth day of the month of Muharram. Although fasting this day is now voluntary the majority of Muslims usually fast.) Some people are quite lenient and lax when it comes to making their children fast. A situation may even arise where the young child feels enthusiastic and chooses to fast and is physically capable of doing so, then his father or mother order him to break his fast claiming that it is out of sympathy. Little do they know that real sympathy is in stressing the importance of fasting and teaching the child about it. Allaah said in Surat ul-Tahreem (interpretation of the meaning): "O you who believe! Ward yourselves and your families off from a fire (Hell) whose fuel is of men and stones, over which are appointed angels stern and severe, who do not disobey the commands they receive from Allaah, and execute that which they are commanded." We must pay extra attention to the young girl when she first starts fasting after she reaches puberty. There is a possibility that she will fast while she has her period (the first time) out of shame or shyness, and end up not making up the days later on.
Also see the Book "70 Matters Related to Fasting".