Read. Reading a copious number of kids' storybooks helps you develop a feel for what is popular and an idea of the writing kids might enjoy. Pay attention to the use of vocabulary, length of sentences, phrasing and description. Try not to imitate the books you read. Instead look to develop your own style by allowing other writers to influence you. This initial step should give you a number of useful tips and some ideas worth pursuing.
Remember that characters are everywhere. You might be waiting for the bus home when you come across a kid on his bike in a character costume. Take your notebook out and jot down his description, then build up a story based on the kid. Ask yourself where he is from, what he loves doing, what he wants to be as an adult, who his best friend is -- you get the idea. Build on a list of exciting and interesting characters based on your day-to-day experiences. Remember that kids love to read about other kids. Stories revolving around children are bound to be popular.
Make the plot character-driven. While a kid reads, he is eager to learn about the character's endeavors. The plot in any good kids' storybook should involve a conflict or problem which must be faced by the main character and how he finds a solution. Make sure the character's attempt to reach a solution is action-packed. Kids generally love a lot of action in fewer words.
Make it visual. The rule that can be applied to all storytelling, and in particular to children's writing, is the rule of "Show, don't tell." Often, kids have shorter attention spans and need to be pulled right into the story from the very beginning. They need to feel what the characters experience. To accomplish this, your dialogue should be simple and realistic, your imagery must be vivid and colorful and your descriptions need to be sensory.