Look in the back of magazines to see if there is poetry in their publications. Submission rules should be printed somewhere on the page or in the Submission Guidelines section of the magazines' websites.
Consider self-publishing a book of your poetry after it's been copyedited. Websites like LuLu.com will publish poetry with no charge.
Inquire about literary magazines, school newspapers or school ezines to see if the editorial team will let you contribute your poetry to their publication.
Sign up to have your book in a poetry collaboration book, such as Creative Communication, Inc. Be careful about poetry books that promise to put your poetry in their books. Although the publishing is free, the books are not, and you are paying for everyone else's poetry too. The bright side of that is if you do like poetry, you get to read your own poetry as well as others.
Enter poetry contests. They oftentimes have monetary prizes and publish your work in a publication. Avoid companies that charge you a registration fee. There are hundreds who won't charge you any money to pick a poem, and you should not have to pay for someone else's opinion.