The info below will give you a general idea of how I come up with my children's illustrations.
Step 1: Thumbnails
Thumbnails give the author and the artist a chance to work out images for the book. They are mini sketches; a preview to show the action on the pages. It gives me the chance to find references, if I need them. They often are revised but it a great first step to get the discussion started.
Note: I work VERY loose on these. I only create them to get a "feel" for the image. Some people have a hard time reading the image, but this is how I work. It's only temporary....
Step 2: Character Sketches, Color Samples and Rough Sketches
The Character Sketches, Color Samples and the Rough Sketches all allow me to work out what the image will really look like. The author or publisher will have the opportunity to see the progress. Revisions are easy and preferable, at this stage.
Step 3: Final Illustrations
The Final Illustrations will be done after we have a full understanding of the characters, color schemes, flow of the story and look of the initial illustrations. At this stage, the ideas are solid enough to move to the final rendering of the art.