Establish a theme for the book. Most publishers aren't interested in books that are a collection of random coloring images. Instead, choose a theme that hasn't been covered much in the past and lends itself to fun images with many vibrant coloring possibilities.
Create the coloring book's drawing. Every coloring book needs lines to color between, or outside of as children please. These images will eventually need to be scanned for digital reproduction, often into a specific format as requested by the publisher, but focus on creating the clearest images possible at first.
Decide on publishers who may be interested in the book. This is where you may need to decide whether to push the book toward a traditional publisher or if self-publishing and internet-based publishers may be acceptable. For now there is less likelihood that independent publishers can offer the support or compensation that traditional ones can. Either way, look into publishers who have a proven interest in coloring books by checking their previously (and recently) published titles. If any of their previous titles too closely resemble your book, they may not be a good match, unless their specific focus is with that topic.
Contact the publisher regarding their submission guidelines. Some publishers may include these online, while others may accept unsolicited material; either way publishers will want to see a sample of the work before agreeing to print the book. Create a sample of the best images, or a completed manuscript, a cover letter and any other materials which may be requested by the publisher.
Develop a marketing plan. While this may not be specifically requested by any publisher, it is always good to determine how popular the book could be and where, how and to whom it may be marketed. If the book's theme is animal based, zoos may be interested, for gardens for plant-based books and so forth. Developing such a plan also demonstrates commitment to the project that can help sway publishers.
Write a query letter to submit along with samples to the publisher. This can include some of the marketing plan but should be kept short, three or four paragraphs (one page) at most. Sell the idea to the publisher as quickly as possible.
It may also be necessary at this point to hire an agent or other representative to advocate for your work. Querying an agent is much like querying a publishing company, except that the agent will rarely want to see the entire book, so prepare the same way as previously mentioned. This step should only be taken if you are pursuing a traditional publishing model as independent publishers rarely require agents.
Send all requested materials to the publisher and wait for a response. Don't be discouraged if the response is negative. Be persistent. Ultimately, if the book is not published through traditional means, self-publishers and internet-based alternatives will likely accept the work with some initial investment and smaller distribution and marketing. However, often self-published work leads to greater compensation on each book sold once expenses are recovered.