When you first finish writing any piece of written work, you're actually only partway done with the process. Publishing your work and getting it distributed to the masses is the next step. With the right mindset and specific goals in mind, it should be possible to get your work out into the world.
Read and reread your manuscript until you feel absolutely confident in it as a finished product. Of course, much can change in the process of publishing, but don't rely on anyone yet. The editors and agents who read your book need to feel confident in it already before committing any energy to its future.
Develop a "pitch" for your book. This should be a short description of the themes, plot and intrigue of the book. Append it to the top of your manuscript.
Find a publisher for your book. The easiest way to find an appropriate publisher is to go to a bookstore and browse through the section of books that matches the genre of your manuscript. Look at the books and see what publishers tend to publish that genre. Write down the names of the publishers.
Another approach is to search the Internet for publishers currently taking unsolicited submissions.
Call up the publishers you've taken note of and ask a knowledgeable person for the contact information of the acquisitions editor. Inquire as to the procedure of sending in manuscripts from an unpublished author.
Alternatively, you can go to the website of the publisher and find the "Submission Guidelines." This will have all the information you need to submit your manuscript. Follow all of this information carefully; you don't want your manuscript to be rejected on a technicality.
Send your manuscript to the publishers, following the specific protocol that the publishers require. Often this will be the pitch and a few pages from a chapter. Be sure to send packages to as many publishers as possible.
Follow up on your packages by calling up the publishing houses--hopefully you will have someone to speak to beyond the secretary at this point. If an editor reads your work and is interested in working with you, they will likely set up a meeting and discuss opinions and changes they'd like to see in the book before they would consider publishing. Check each publisher's guidelines before calling, as some discourage this.
Keep trying. You will get many rejection slips back the first time. It will probably happen the second time, and the third time too. Just keep submitting. Keep researching and finding more publishers, keep revising your pitch and manuscript, and eventually you will find the right fit. Just don't stop sending the manuscript out--it can't get published if no one sees it.