First off, compilation implies 'multiple sources.' If you have written all the poems yourself, it is not a compilation, it's a "manuscript." But you're way ahead of yourself. Back up.
Well before you go for a full length book, see if you can get just one or two poems published in a *reputable* literary magazine. Clough is incorrect in regards to agents. Agents work for money and, frankly, there isn't any money in poetry. For example, a best seller in fiction must sell 100,000+ copies, whereas in poetry, a best seller needs to sell only 10,000+ copies. All you need to publish a poem is a good poem and a list of editors to send it to. I suggest "Poet's Market" for that - it's updated every year and contains all the information you need to get started.
Bare in mind, even if you're a top notch poet, the competition is fierce. Any good lit mag will receive thousands of submissions a year. A big part of being a poet is getting rejected way more than you are published.
Once you have published quite a few poems in literary magazines, you can submit those poems and a few more as a complete manuscript to a contest. If you win, they publish your manuscript as a book and give you a little money.
Or you could fork out bunches of cash at any printer and make vanity prints. They're overpriced and rarely worth it, but it's an option.
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