My work process begins when the publisher gets in touch with me. It used to be a phone call, now it's an email. The books that I illustrate are generally already written and scheduled for publication before the publisher contacts me. I am given a schedule, naturally, and I usually sign a contract before the work begins. Sometimes I am paid advance and royalty, and sometimes by flat rate with no royalty. I rarely have any contact with the author.
First, I do rough sketches. I used to start with "thumb nail" sketches (sketches done much smaller than actual size, maybe 50%), but these days I usually start with full size rough sketches. After the art director sees the rough sketches, I make any changes that the art director would like, and re-submit the revisions to the art director. When the rough sketches have all been approved, I create the finished art. Sometimes there are revisions on the finished art as well. I often receive layouts with text in place from the art director. I can usually move the text around as the composition develops.
When illustrating children's books, it's usually a good idea to keep the compositions interesting by zooming in or out, changing the perspective, and keeping the action moving from left to right.