At its simplest, prayer is simply talking with God -- something any child can do. Jesus made it clear that he'd like everyone to keep it just that simple, as noted in Matthew 18:3, when he called a child to himself and said, "Truly I tell you, unless you change and become like little children, you will never enter the kingdom of heaven." When you teach your children to pray, focus on teaching them to speak to God naturally and in their own words, as they would speak to their father or a trusted friend.
Teach your children to give thanks to God for the everyday blessings he gives us, such as friends with whom they can play, food to eat, parents to take care of them and favorite toys. Teach your kids to take a moment to say, "Thank you" to God when something good happens. Explain to them that we can even thank God when things aren't going our way. First Thessalonians 5:18 teaches us that it's always God's will for us to give thanks.
Everyone says and does things that they sometimes shouldn't. At a very young age, start teaching your children that God will forgive them and help them to change. Read 1 John 1:9, which deals with this, to them. Explain to them that they should pray to God for forgiveness when they do something they shouldn't. When teaching kids about God's forgiveness, make sure they understand that they might still have to apologize to the people they hurt -- and that there might still be consequences for their actions, but they can know in their hearts that God forgives them.
Praying for Needs
In John 15:7, Jesus teaches us that if we abide in him, we can ask for whatever we want. That's a powerful promise, especially when combined with the faith of a child. Teach your children that they can ask Jesus for anything. Of course, it's also important to teach them that God knows what's really best for us and He may sometimes say, "No" for reasons we don't always understand. Teach your kids that when they pray for their needs and desires -- or the needs of others -- to always follow Jesus's example and pray, "...not my will, but Yours be done," as noted in Luke 22:42.
Praying for Enemies
It's not unusual for kids to be teased, picked on, bullied or otherwise mistreated by others from time to time. In Matthew 5:44b-45a, Jesus teaches to "...love your enemies and pray for those who persecute you, that you may be children of your Father in heaven." If your kids have trouble doing this, be patient with them. Set an example by letting them see you pray for people who mistreat you. With the right example and a little encouragement, children will generally start to develop the kind of Christ-like character that will allow them to sincerely pray for others, even when others are mean to them.