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 Rough Sketches
The Character Sketches allow me to work out what the image will really look like. The author will have the opportunity to approve and revise the image. Revisions are easy and preferable, at this stage.
Note: This sketch was done on drawing paper and adjusted with tracing paper while I work out ideas. But I often use my computer to make things easier.