Choose a theme or topic for the book. If you need inspiration, read other children's books, watch movies, take a walk in the park or even talk to a child.
Decide how long your book is going to be, and who your audience is. Is it going to be a couple hundred pages and for 10-year-olds, or only 10 pages and meant for two-year-olds? The longer your book is, obviously, the more work there is to be done within the month.
Work out a rough outline. Some writers like to write as it comes to them, and others require a detailed outline before they begin. Do what works the best for you, but if you are going to finish your book in only 30 days, an outline is needed so you know where your story is headed.
Set a strict schedule for writing. It doesn't matter whether it is number of words written or time spent writing; what your exact schedule ends up being is up to you. But when you decide to write, you must stick to this schedule -- don't answer the phone, mop the floors, or decide to go out shopping.
Write your story. How much needs to be done depends on your personal choices, but one of the hardest things for many hopeful writers to accept is that there is no secret to writing a book. You just have to sit down and do it.
Motivate yourself with whatever means necessary to stay on schedule. Promise yourself a nice dinner when the book is done, ask a friend to check up on your status, or shut yourself in an office away from distractions.