You've written a children's story. Everyone thinks it's great. What do you do? Research the publishing industry.
Children's stories can be very difficult to get published. Publishers receive hundreds, if not thousands, of submissions each month. What you need to do to help your chances of getting published is research the industry and learn how to approach publishers.
The Purple Crayon (http://www.underdown.org/), a website by Harold D. Underdown (author of The Complete Idiot's Guide to Publishing Children's Books), takes beginners through the jungle of the publishing world. The website features of number of articles covering traditional publishing and self-publishing, current trends in children's books, sending out multiple submissions, and more.
There are a lot of good articles to read through, so grab a cup of coffee, get comfortable, and begin.