I think the Writer's Market book would be your best bet. It's a big thick book published every year, that tells how and where to get your work published. You can also visit their website at writersmarket dot com.
I have to agree with this poster. The Writer's Market is an excellent tool when wanting to look for a publisher. My publisher handles poetry and short stories mostly. Funky stuff. I was fortunate to find him. A friend referred me. So, both of my poetry books are published by the same company and I did not pay anything. Granted it is a small company and I have yet to make money from them. Having them in print is what was most important.
There are publishers who charge. This is called subsidiary publishing. Basically, the publisher does not feel confident that the book will sell, so they charge the author fees to help cover the cost.
L. Frank Baum wrote the Wonderful Wizard of Oz. Believe it or not, he himself paid to have the book published because NO publisher wanted it. Every single publisher turned him down. He coughed up the money to pay for publishing costs, and the rest is history.
He is not the only one. Many authors of the past had to pay to have their works published, and later became famous.
It also helps considerably if you have minor publications elsewhere, this way you can present your work with a type of "writer's resume". I have several poems in magazines, poems in anthologies, an article in a periodical, and two photographs published, plus the two books I have. I have not written much since my second book (it took the winds out of me), but I am thinking of starting a newsletter. (I probably would be doing that now, but my printer is on the fritz.)
Finding a publisher can take a heck of a lot of time.
So...get the Writer's Market;
Join a writer's community forum and maybe let a member read an excerpt of your book. You never know, someone may refer you to a publisher.
You might consider picking up the Writer's Digest Magazine. It often lists contest and publishers looking for work. I know there are many contests for first time writers. You may qualify for some.
Always include a cover letter with a synopsis and some of your past writing experience.
Always make sure the manuscript is in proper form. If it is not, it will be turned down.
I hope you find someone! Good luck!