I've published poetry and articles. Poetry through contests and through an anthology that was organised through a writing website that I am a member of. Articles by basically being cheeky and pitching ideas to online media websites.
With poetry contests, it's good to be careful. There are genuine ones out there, and ones that will publish anything and everything and then want you to pay a fortune for a copy of the publication. So that's rather pointless, as it says nothing about your work.
With books, it's also good to be careful of the vanity press, where they'll publish your work, but you have to pay for it, and do your own promotion. You'll usually end up out of pocket. That's happened to a couple of friends of mine.
There are genuine small publishers out there, though. I've done editing for an American one in the past.