Find out how many pages are going to be in the children's book and how many illustrations will be required for each page. That provides a framework for the work you need to provide, as well as a sense of how much time you should to devote to the project.
Read the text that will accompany your illustrations, and work with the author or the publisher's art director to break it down into sections. Each page of the book contains a set amount of text, and your pictures on that page need to match what it describes. The illustrations must also fit within the specific space allotted. If the text is being superimposed over your artwork, you must provide an appropriate space in your illustrations where it can be placed without disrupting the action (i.e., not over any characters, important objects or key events). If you are working for a publishing house, the art director will likely have a basic layout prepared. If you are self-publishing, you should work with the author to determine how much text is on each page.
Identify important characters in the story and develop a specific look for them. Most children's books have a limited number of characters. The protagonist or hero will likely appear in the majority of your illustrations, and other important characters will have a role to play as well. Your art needs to reflect their personality as perfectly as possible.
Develop a color palette and tone you will use. Artwork in children's stories needs to have a unifying "look" that will draw the eye and enhance the overall theme of the work. The specifics depend on your particular style and the content involved, but should generally be bright and cheerful. Discuss the specifics with the art director or the author so that you both understand what is entailed.
Sketch out each image in pencil, conveying the action reflected in the matching text. Show the sketches to the art director or to the author and work with her to revise or alter the images until you are all satisfied with them.
Finalize the sketches and then paint or draw the final illustrations using oils, water colors or whichever method you have agreed upon.