There are a number of different ways, but as you probably know, a lot of people want to publish a childrens book. It is hard to get noticed.
I went to a writer's conference once where an agent (a long-time, big name in this arena) for childrens books was firmly against anthropomorphic animals and rhyming.
That pretty much knocked me off her list.
My friend and I decided to spit the cost of having a quality book printed, and because we had a niche to market to-- we managed to cover our costs and make a small profit. (The satisfaction and feedback was priceless.) I've written a couple of hubs on the subject. Check my profile page.