For the author it is quite natural to show off your creations to others, and ideally to see them published in the newspaper or poetry collection. Fame, recognition, fame and fees is clear and correct explanation that should be followed to become a recognized poet. There are several ways to publish your poetry.
In the Internet there are many poetry sites, love to host poems by beginners. In order to be able to published here, you need to register it, which, in particular, will protect your work by copyright. Getting access to the page, you can publish the poem, read and comment on poems of other authors. In addition, for a fee, the website being temporarily placed on the main page a link to your poems.
The second option is to create your own website or blog (online diary) where you will have the opportunity to publish whatever we want. Please note that beginning readers will not be very much, but if your works are really good, soon the number of visitors to your page will increase.
As for paper publications, all in the same Internet regularly holds poetry contests on various topics. As a rule, the winners of these competitions get the opportunity to publish their poems in a poetry collection. Of course, you need to carefully read the terms of contests and participants, not to get caught by unscrupulous organizers.
Finally, one can find literary magazines or Newspapers sometimes accept poems by unknown authors to be published on the last pages. Basically, these editions are supported afloat at the expense of enthusiasts, so the fees and the royalties are better yet not to think, but at least your work will be seen by the readers. If works, according to experts, better send them in serious literary publishing.