Choose your audience. What age group do you wish to write for? Begin your research at a local library or bookstore to see what types of books are successful and popular for children of those ages. Take notes on trends and anything that seems interesting.
Practice writing by keeping a daily journal or doing writing exercises. Begin making rough lists of any ideas that come to mind.
Choose an idea and begin to outline it. Make sure you have developed characters and a planned beginning, middle, and end.
Write a complete draft. Don't worry about format or pictures, simply get your story on paper.
Ask for help. Have honest friends edit and critique your work. If you have young family members or friends with small children, read the story out loud to them and see how it is received. Make any necessary changes to improve your story.
Find a publisher. Use your previous research to learn which publishers tend to prefer which types of childrens books. When you've found some that fit your story, check their websites to find their writer's guidelines. If you can't find them easily, you can send a request for them.
Follow the guidelines very carefully and submit a carefully edited manuscript.
Wait for a reply. Writing childrens books is a competitive field, so don't be discouraged if you don't hear anything right away. Instead, keep practicing and honing your writing talent, and start again.