Understand the age group you're writing for. Publishers look for age-appropriate material that offers basic life lessons to their young audience while entertaining them at the same time. Regardless of the age-group you write for, your first priority is to engage them and your second priority is to educate without preaching or talking down to them. This is the type of children's book you can market.
Find a publisher appropriate to your material. You can do this by purchasing the "Children's Writer's and Illustrator's Market" by Writer's Digest Books. You can also consult an online directory of publishers for children's books (see resources). These market listings tell you where your markets are, what type of stories the market looks for, how to contact the market, how to submit your material, and how much you will be paid. These market resources are essential to your children's stories writing career.
After finding a publisher appropriate for the type of book you've written, submit your manuscript according to the market listing guidelines. Include a brief query letter whether the guidelines request one or not. Introduce yourself in the letter, briefly describe the manuscript you're submitting for consideration, then close by thanking the editors for their time. Follow market listing guidelines regarding how long it will be before you can expect a response to your submission. If your manuscript is rejected, don't get discouraged. Try a new publisher.