Decide what kind of children's story you want to write. Find books at the library or any bookstore that detail the specifics of writing for children. You can also find online reference guides you might want to keep handy as you develop and begin writing your story. Writing for children is different than writing for adults, so keeping a set of rules in front of you will help to keep you focused on your intended audience. The guidelines for children's writing could even inspire a good idea. Make notes regarding your story idea and keep them in front of you.
Write your story. Use an online word processor if you want to write your children's story online. Google Docs is a free, full-featured word processor that's web based (see Resources). If your children's story is a picture book, Google Docs allows you to insert graphics to your work, so you can completely format your book online.
All of your work is saved online, and you can access your story from anywhere at any time. There's no need to download and install anything on your computer. Sign up for your free account and start writing and formatting your children's story immediately.
Submit your finished work for publication. Do this online as well. The best avenue to pursue is the Writer's Market. There is a small monthly fee to join, but the database is updated every day with publishers looking for new material. The database publishes complete guidelines for submitting your children's book manuscript, including who to address in the submission, where to send the submission and how it should be formatted. Writer's Market also includes information about royalties and advances. For the best chance of publication, submit to markets that accept the kind of work you have done and carefully follow the guidelines for submission.