There are four routes you can go: try to sell the volume as a book to a publisher, publish 2-3 poems at a time in "little" magazines and build a reputation, self-publish a book, self-publish on the internet. These are in order from hardest to easiest to accomplish.
Without a name as a published poet, you're not going to publish a book of poetry so the first option is out. Seriously, you'd be wasting your time.
Most literary poets publish in so-called "little" magazines (the second option), then move up to the big time publications like New Yorker, Poetry, the major reviews. You need to be very talented to make it via this route; and talented means being able to recognize what's bad in what you've done as well as what's good. A writer who doesn't dump 80% of what he/she writes into the circular file isn't a writer In my opinion. A sizable portion of T.S. Eliot's The Wasteland (one of the 20th century's greatest poems) was red-lined by Ezra Pound, and Eliot followed the Master's advice and retained the editing. This is a long road, and you'll have to be patient... and realize that many very good poets never make the big time.
That leaves self-publishing. A good way to do this if you want to publish a book is via either
Lulu or
CreateSpace. You can print copies on demand, and they provide ways of marketing your book. If you'd like to publish them in small groups, there are quite a few
online literary magazines out there. Check out any collection of poetry by a contemporary like W.S. Merwin, Galway Kinnell, Jorie Graham or Mary Jo Salter; you'll see a number of publishing credits for the poems in the volume. Most poems in published volumes first appear elsewhere. Even well-known poets publish by the little/literary magazine route.
EDIT: I wanted to leave you with some encouragement - the following is advice given one of my favorite contemporary poets, W. S. Merwin, by one of his mentors, John Berryman:
... as for publishing he advised me
To paper my wall with rejection slips
His lips and the bones of his long fingers trembled
With the vehemence of his views about poetry
He said the great presence
That permitted everything and transmuted it
In poetry was passion
Passion was genius and he praised movement and invention
I had hardly begun to read
I asked how can you ever be sure
That what you write is really
Any good at all and he said you can't
You can't you can never be sure
You die without knowing
Whether anything you wrote was any good
If you have to be sure don't write
--- from "Berryman", by W. S. Merwin