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 practice of the first women of Islam who were living around the Prophet, salla Allahu alaihi wa sallam. An example of that is 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 Ramadan, 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 practice it easily 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 up to 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 achievement.

Let your children (those that will not disturb others) go with their father to the Masjid for Maghrib prayer and break the fast with the larger Muslim community to make them feel the greatness 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(those that will not disturb others) 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 Ramadan.

Teach them to recite Qur'an regularly and inform them that the Prophet (Sallallahu alaiyhi wassallam) used to do that in Ramadan (more than that in other months).

Correct them if they behave wrongly or say unacceptable words and remind them that they are fasting or they are in Ramadan 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. [al Bukhari and Muslim]