Set a budget for your children's puzzle book-publishing process. Each self-publishing company will have different rates, and you should have a financial limit in mind before choosing one. Visit self-publishing websites like such as Lulu, iUniverse, and Author House to find one that suits your needs best.
Make a plan for your book once it's published that details how many copies you want, and how widely you want them distributed. Keep in mind that you will be responsible for the marketing and promotion of your book, which should be included in your budget.
Register your puzzle book for a copyright (see resources). In most cases, a self-publishing company will not take care of this step for you.
Sign up as an author on the self-publishing company's website that you have chosen and upload your puzzle book according to their specific guidelines. Once you have proofread your book, submit it to the self-publisher for printing.
Consult Publisher's Marketplace to find editors and publishing houses that publish puzzle books for children. If you have a favorite children's puzzle book, check the inside cover to see which house published it. Publisher's Marketplace will have the contact information for the publishing houses.
Prepare your manuscript, which may vary depending on the house's guidelines, but will generally need to be a word document with a title page that includes a title for your book, your name and contact information. Write a query letter describing your puzzle book, including a short bio of your writing and game-making career.
Mail or email your manuscript and query to the publishing houses and wait for a response. In some cases, the house may only want a query; abide closely by the outlines set forth on Publisher's Marketplace. The publishing industry tends to move slowly, and it may be months before you hear a response.