Ask an objective third party (preferably a published author) to review the child's book and advise you on its strengths and weaknesses. As a parent, relative or teacher, you probably have somewhat of a bias on the quality and originality of the story and its illustrations and need an honest assessment as to its realistic chances of getting into print. If you don't know any published writers personally, the websites and forums found in the Resources section of this article will help you connect with individuals who'd be happy to read a sample page and tell you what they think.
Study what the competition is doing by visiting the children's section of your neighborhood bookstore or bookmarking websites such as Kids Read, Too! (see Resources). Make note of who the publishers are for these books.
Purchase a copy of Writer's Market, an annual resource published by Writer's Digest Books. You may be able to find a copy in your local library. Look up each of the prospective publishers you made note of in Step 2 and read their submission requirements. The listings will also advise you of the desired word count, recent releases and whether the book has to be represented by an agent. If you decide you need an agent, a good place to start is at Agent Query (see Resources), which lists which representatives handle children's books.
Make a list of the publishers and/or agents that are a good match for your child's book.
Research submission guidelines for manuscripts. While more and more agents and publishers are accepting electronic transmissions, never assume that this is the case unless it is spelled out in their submission requirements. Nor should you resort to informality and chattiness if you do approach them via email; your query and subsequent correspondence should be just as formal as it were being sent via snail mail.
Compose a one-page cover letter that introduces yourself on behalf of your child, briefly summarizes the book's content and why it is unique and concludes by identifying the word count and the number of illustrations (if any).
Include a self-addressed, stamped envelope with every submission. If you want the material returned, make sure the envelope is large enough to accommodate it.
Research alternative publishing options if (1) the individual you consulted in Step 1 advised that the book wasn't commercially viable or original, (2) you're not getting any nibbles of interest from publishers and agents or (3) the nibbles you're getting have all turned into rejection letters. Some of the options include self-publishing entities, ebooks and CD-ROMs. (The links at the end of this article discuss the benefits and liabilities of these venues.)
Survey local print shops to see what it would cost to print and bind the book yourself. In most cases, a book written by a child isn't going to be that long and, furthermore, will probably be given to friends and relatives who will treasure it just as much if it were published by a traditional house.
Produce the book as an ebook or CD-ROM yourself. Depending on your child's age, you may even want her to participate in the on-screen design and placement of text.
Serialize the book on your own website. This can either be open to the public or password protected so that only friends and family can access it.