Children (who did not reach puberty) are not commanded to fast.
However, their parents or guardians are strongly recommended to
encourage them to fast few days so that they get used to it and they
grow up knowing of the worship of fasting as they would know that of
praying. In fact this was the practise of the first women of Islam
who were living around the Prophet, salla Allahu alaihi wa sallam.
An example of that is ar-Rubayya' bint Mu'awiyyah who reported that:
"The Messenger of Allah,salla Allahu alaihi wa sallam, sent a man on
the morning of the day of 'Ashurah, to the residences of the Ansar,
saying: 'Whoever has spent the morning fasting is to complete his
fast. Whoever has not spent this morning fasting should voluntary
fast for the remainder of the day.' We fasted after that
announcement, as did our young children. We would go to the mosque
and make toys stuffed with cotton for them to play with. If one of
them started crying due to hunger, we would give them a toy to play
with until it was time to eat." [al-Bukhari and Muslim.]
There are many ways to educate your children about Ramadaan, the best
and most important of which is to set the good example by fasting
properly and behaving according to the Prophetic teachings. This is
what your children will take from you first. When you are fulfilling
this you can very easily [and they will accept it and practise it
easilly as well] teach them what you want. Here are few tips that
you can use with your children [you can think of others as well]:
Depending on their age encourage them to fast a number of days upto
every other day or more for those who are almost at the age of
puberty. For those who are still young let them fast a day or two
and praise them in front of friends and relatives for their
achivement.
Let your children go with their father to the Masjid for Maghrib
prayer and break the fast with the larger Muslim community to make
them feel the gretness of fasting and the unity of Muslims in
worshipping Allah.
If your children cannot fast let them eat with you at the time of
Maghrib and teach them that you are breaking the fast even if they
ate before.
Teach your children the supplication of breaking the fast
Take your children to the Taraweeh prayer so that they get used it
and know about it from their early age. They may sit or stay in the
back of the prayer room if they get tired.
Teach them to give charity. Do it in front of them and tell them you
are doing it because the reward increases in Ramadaan.
Teach them to recite Qur'an regularily and inform them that the
Prophet (Sallallahu alaiyhi wassallam) used to do that in Ramadaan.
Correct them if they behave wrongly or say unaccaptable words and
remind them that they are fasting ot they are in Ramadaan and this
may alter their reward.
Wake them up for Suhoor [even if they don't fast] and Fajr prayer.
Teach them to feed the people fasting and tell them about the reward
for that.
Dress them in the best clothes, give them a bath and take them with
you to the Eid Prayer. Teach them that this is our feast and
celebration and that christmas, easter, thanksgiving and other
holidays are not ours. Stress the distinction.
and remember that the Prophet salla allahu alaihi wa sallam said:
"One who is given the responsibility of the bringing up of daughters
and treats them well will be a shield for him from Hell.