Let's be honest. Reading poetry, in
Anyone can read and enjoy and comment appreciatively and intelligently about poetry. You don't have to be some sort of creative writer, or a poet, or an artist, or sensitive, or anything much, beyond a thoughtful reader.
I hated, loathed, and detested poetry for much of my life; it wasn't until I read this poem that I realized poetry doesn't suck. If you like music with lyrics, if you like songs, then you like poetry. I think I thought I hated poetry because of the way poetry was presented to me in school, where teachers spent hours trying to explain meter, and scansion (it's not that big a deal, and you can read and like poetry just fine without knowing anything about meter or rhyme).
Moreover, no matter what your English lit prof told you in college, and despite that sophomore English teacher who also told you that splitting an infinitive would send you straight to Hell said—poetry has a multiplicity of possible readings. There are lots and lots of ways for people to read the same poem; they're all valid, as long as readers can tie their response to the poem. Even "I don't really like this poem because it brings up a really unpleasant memory" is a valid response for that person at that time to that poem.
What then do you talk about with a poem? Well, to start, you can talk about what you notice about it. Is there a particular line or section that draws your attention? Is there something that reminds you of something in your life, or perhaps something else you've seen or read? Are there any patterns, or sound, or words, or imagery that you find interesting or that attract your notice? Is there someting that you just simply like about the poem (or dislike)?
Because poetry by its nature is compact, compressed, and eliminates excess words, it's particularly fun to look for patterns. Patterns of image, and metaphor, of sound, and rhythm—and perhaps even more interesting to look for places where the poet sets up a pattern, and then changes, or departs, or alters that pattern.
If you want something a little more formal, here's a getting started guide to writing about poetry in academic terms. Me, I'd rather just talk about why I love a particular poem, and how it works.