The question that poets probably get asked the most in workshops is how to get published. There are thousands of articles, hundreds of books and an endless amount of advice that is shared about how to get published.
I'm sure there is good information in all those places, but I would say the best answer is that you have to write good poems and you have to send them out regularly.
No one is going to come up to you at a reading or at your writing desk and ask for a poem or manuscript for them to publish. That is the one in a million kind of story I associate with starlets being spotted by a director at a soda fountain on Hollywood Blvd. in the 1930s.
We can offer a few places to look for places to publish.
How about this appealing headline: "1,290+ Literary Magazines Ready to Publish Your Work?" That was the tagline for the Literary Magazines database at Poets and Writers magazine. You can use it to research publications before submitting your work, and then use it for deadlines for contest and submissions.
It has a wide variety of publications, from the well known to the never-heard-of: That Literary Review is interested in "creative nonfiction, fiction, and poetry of the mysterious and the wonderful." New Letters seeks "creative nonfiction, fiction, and poetry regardless of subject, style, or genre." Your Impossible Voice publishes "brash and velvety new work," including creative nonfiction, fiction, and poetry.
Poetry Mountain also has a list of literary magazines, as does poetrykit.org.
Again, the secret is sending out your work. Prepare for rejections. A baseball player only has to hit once out of three at bats to have an excellent .333 batting average. For poets, one acceptance for ten submissions would make you an all-star. But you have to take some swings.