Comprise your child's work. Take anything and everything that your child has written and make a book out of it. Even if you simply purchase a three ring binder, this will suffice and will be a way to preserve and collect their work. When the time comes to submit writing samples to a publisher, you will have them all in order and readily available upon request.
Locate the right publisher. There are many magazines and Internet publications that are geared toward children and their works of poetry, prose and fiction. One way to find these publications is to read the book, "Market Guide For Young Writers." This is available at your public library or for sale on Amazon. Some magazines that gear their publication toward children are Stone Soup, Merlyn's Pen, Potato Hill Poetry, and Creative With Words Publications (see Resources below).
Ask about requirements. Many publishers and magazines have editorial preferences and guidelines they want in order to publish your child's work. It is necessary to find out what these guidelines are before submitting your child's work to them. Some require a minimum or maximum word count, some only publish certain age groups and some will only accept a specific form of writing such as fictional stories or poetry.
Send a query letter. When you believe that you have found the publisher for your child, send out a query letter. This is something that will introduce your child and their work to the prospective publisher. Make sure that it is set up in the business letter format, make it direct and concise (about a page will do), and include your personal information like name, address and phone number. You also want to address it to a specific editor. You can find out who this would be by calling the publisher of your choice and requesting that information.
Publish locally. If you are having difficulty finding a publication for your child's poetry, try starting out locally. You can call the Council of English Teachers in your state to start with. They will sometimes sponsor a book of creative writing annually. You can also ask local banks and businesses if they would mind your child posting some of their work in their hallways for the public to see. Anything that will help get your child known for his/her work is as good as being published.