As with any website design, when designing a site for children, you must always consider your audience and build it with them in mind. A website that will predominantly be used by children must be easy to navigate through and laid out in such a way that they understand how to get from one area to another and back again. It is important to keep the content clean and clear and not try to be too fancy. Children often like to see bright colours and moving areas of the site, but overdo it and they may find it too confusing.
If the site is going to be used by children of varying ages then you may want to split the site up by asking the child to choose their age group first. This can then allow you to really specifically tailor the content that is shown to them so that it fits their ability.
If the site is an educational one, then you may want to include some simple games that they can play to ensure that the site is not only educational but also fun to use. When considering your navigation, younger kids generally prefer image and character-based navigation whereas older children may be able to read though a list of options available to them or use a search function to find what they need.