Namely... how in the world does someone publish poetry? Is it similar to how one would publish short stories? Or... something completely different?
It's pretty much the same as publishing stories. You submit to magazines (or other media) that accept poetry. Check out duotrope.com for a listing of poetry (and short story) markets.
It's a little different, but not by much. I think the two main differences are: 1. Poetry generally pays less. 2. The majority of magazines accept poetry in bulk. I would just make sure that the magazine actually accepts poetry, and that you read the submission guidelines before submitting. I'd suggest picking up the 2012 Poet's Market for some tips, and for applicable poetry market's.