If they try hard enough, someone will publish their poem in a magazine or book, although to be published in a book nowadays, the poet usually has to pay the publisher. The publisher will make his money by selling the book of collected poems back to the poets, generally the only ones who will pay to read poetry but only if it is their own. Although there are some genuine publications for serious poetry, only in songwriting is the competition still fierce, and the rewards large. But remember a songwriter is a poet and poetry is still an art. Poetry deserves a lot of thought and the best words that are in you.
Artists look at the world and summarize or re-interpret it for everybody else.
To do this well, you must often bend the rules, both of grammar and of the world. So don't feel constrained by your words but try to set them free so that someone else can experience something new or learn more about themselves. Writers talk about the muse, as a spirit that brings the ideas and words to them and it really does seem to work that way, especially when your muse has left and you haven't got a single idea in your head. Then start playing with some old ideas or put down a few new ones and see what happens. I have had songs almost leap out of me, done in 45 minutes.