First you have to come up with a great idea. You have to let the idea float around in your head for awhile. Most good ideas will stay with you for a least a couple of days. When a new idea pops into my head I usually write it down in a note book. You never know when some bad ideas can be turned into good ones.
If it really was a good idea, I begin to rough out the story. Because I'm an illustrator by training, I usually know what the characters look like, but I still have to build the story around them. Rewriting can be really awful but it's really important.
Once you're done the story you can (if you're a good illustrator) layout a 'dummy book'. My 'dummy books' are 8.5" by 11". They're blank books. Most folks don't know that a picture book is either 32 pages or 24 pages. That's the rule so don't make your book longer or shorter. Just like writing, drawing takes patience. I do a lot of revisions before the pages look just right to me.
Once you have your 'dummy' or story done, it's time to send it out to the publishers. Make a lot of copies of your work and send out the stories to a lot of different publishers. If you want to start small though, just pick one and send them the story. You'll have to include a self-addressed stamped envelope if you want a quicker reply. The publishers address can be found on the copyright page of most books.
The biggest mistake people make is not sending their work. You can't get published if you don't send it.
Be patient. 5000 children's books are published every year. Editors at big publishing houses receive about 2 times that many stories to review every year.
When the letter comes back from the publishers it might say NO THANK YOU. It doesn't mean your story is bad, just that the editor who read it didn't think it was right for the publishing house. Just pick another publisher and send off your story again. I get rejected to this day. I received about 100 rejection letters before I got my first book published.
If you're lucky... they'll say YES! and agree to publish your story. Thank your lucky stars you've just joined the club. If you wrote the story, they'll find a good illustrator. Just sit back and let the artist work.
(Oh yeah... Remember, you don't go into children's books to become a millionaire. So hope your book sells well and move on to your next idea.)