Trying to publish poetry can be extremely frustrating, but the simple key to getting poetry published is persistence. Every person will be touched by a different kind of poetry, so there is no single "correct" way to write poetry that will make publication more likely. Finding a magazine, anthology, or other publication that is a good fit for your poetry is also important, as different types of publications tend to publish poetry that feels very different. Research into the kinds of poetry that are popular and working to build up an impressive history of publications can make it easier to get published, but many poets find that staying true to a personal vision wins out over getting published most of the time.
The first step to getting your poetry published is writing poems. If you have been writing for a long time, then selecting from poems that have already been written is the best strategy. On the other hand, a person who has only just begun to write poetry may have better success working diligently on a single poem until that poem is satisfactory, then moving on to the next one. Most poetry publications ask for several poems in a single submission, so it is a good idea to have more than one poem that you would like to publish.
Submitting poetry is the most important part of trying to publish poetry, but it is also the most frustrating. Many poetry publications can take months to respond to submissions, although there are some that respond faster. It is a good idea to cast a wide net and submit to many different publications, always making sure to follow the guidelines provided by each publication. In order to publish poetry, you must get used to following strict submission guidelines so that the writing rather than the formatting can shine.
While it might seem oversimplified, submitting poetry is the only way to publish poetry. The submission process has a number of different aspects, including dealing with rejection and anticipation. Some magazines are more prestigious than others, and getting into publications with lower barriers to entry can help build up a poet's portfolio of published work. Finding online journals, anthologies, contests, and other places that will publish poetry also helps poets learn about work that is currently popular, and may improve the poet's craft overall.
One alternative to this endless cycle of submitting poetry is to publish your own poetry, although this is sometimes less satisfying than having work accepted for publication. If you decide to publish your own poetry, it is usually best to format the poems in a small book of some sort or put them online. Marketing this type of book is often difficult, but some people find success on this path. Even people who self-publish poetry often find that it is a good idea to continue to submit to other publications, as these other publications can provide publicity for a self-published book.