Research the market. Go to bookstores, libraries and search online to locate other books about origami similar to the one you want to publish. Note the publisher of each origami book. Keep a list of these potential publishers for your book in a journal. You can also find lists of publishers in reference guides for writers. Remember to focus on publishers that specialize in origami or related types of art.
Ask if any publishers or agents are interested in your book. The protocol for publishing nonfiction is different from protocol for works of fiction. You may want to find a publisher or an agent, who will try to sell your book to a publisher before you write your book. However, even if your origami book is already written, you can still solicit interest. Contact each publisher and ask for submission protocol. Note the details you are given in your journal and follow them exactly.
Follow up on your submissions. Review the notes that you have written in your journal and contact each of the publishers and agents who accepted a submission about your origami book. Remember to give the publishers and agents enough time to review your book before you contact. Be courteous and professional. If you are offered a contract for the production and sale of your origami book, review the terms before you accept.
Consider self-publication. If you do not find a publisher interested in printing your origami book for you, consider having it printed on your own. Self-publication will require an initial investment, but there are many options. Research do-it-yourself methods as well as self-publishing services that will print your books for you. As a self-publisher, you will have to market and sell the books you publish, but with adequate research, preparation and realistic expectations, self-publication can be a successful route.