Now we are getting into an area where I am not too knowledgeable. However, I can still provide my experience.
As much as I would love for a publishing company to take me in and publish my work, that is not an easy task. I'm not exactly sure the best way to go about it. Instead, I chose to do online publishing.
Amazon.com is where I started. They allowed me to easily publish an ebook version on my novel on their website. The process is free and was not too hard. It is cool to see your item on Amazon.
There are other site to online publish with - I also used one called Smashwords. This site is nice in that they make your book available at Barnes and Noble, ibook, Kobo, and other places automatically. They are free as well. That said, I have had more sales through Amazon.
What about a hard-copy of your book? Amazon owns a company called createspace that will do this for you. You provide the manuscript, the front cover, and the back cover (or choose one of their pre-formatted ones) and they will make the rest happen. Again, this is free. I just did this in the last few weeks and the hardcopy (along with the original ebook) is already on Amazon.
Of course, I bought a copy of each of my books (the author gets a good price), and it is truly awesome to hold your own book!