You've finished your book. Congratulations! Now, get to work. Go back over your manuscript and make sure the grammar, spelling and punctuation are perfect. Then edit the content to make sure the book is the best it can be. If you're not confident in your editing ability, consider hiring a professional editor to whip the manuscript into shape. If you are writing fiction, you will need to finish and submit a complete manuscript. If non-fiction, a sample chapter or two is sufficient if it's accompanied by a proposal.
Write a query letter for potential agents or publishers. The goal of the query is to outline your book and entice the agent or publisher to request the manuscript. Do not send the manuscript or full proposal. It will not be read. You will have more luck getting published if you are represented by a literary agent. Traditional publishers typically will not even consider reading a book or proposal from an author who is not represented by an agent.
Identify appropriate agents or publishers for your query letter. Do not send a a science fiction manuscript to a publisher who specializes in romance novels. If you're proposing a memoir, make sure your potential agent represents authors who write memoirs. Get a copy of "Writer's Market" to research agents and publishers or go to the AgentQuery website to research potential agents. Pay attention to their submission guidelines. Some accept email, some do not. Follow their instructions when submitting your letter.
Now wait. It can take from two to six months to get a response from an agent or a publisher. It typically does not help, and could even hinder your chances of acceptance, to call or write asking if they are reading it. While you are waiting you can research the audience for your book, research other agents or publishers or edit your work. Or you can always get started on your next book.