Those are interesting questions. I almost always recommend Pinsky's The Sounds of Poetry and Dobyn's Best Words, Best Order for people looking to understand what's going on technically, as described in layman's terms.

I'm not sure if that is possible, as one of the basics of poetry is the play on perception and expectation. Thus, no one poet's work will illuminate all other works. I think that The Collected Poems of Frank O'Hara might be a good place to begin building an understanding of how a lot of contemporary poetry was formed.

I also think though, that being familiar with the basics of appreciating painting (and other visual arts) and music (in a more in-depth sense than putting music on for background noise) also help to understand poetry.

Then again, sometimes people immediately "get" particular poems, whether it's due to their own habits of expression or imagination, or where they happen to be in their lives when they read those poems.

Poetry's a slippery thing, both on purpose and by design and because of its inherent nature. I'd be interested to get other people's ideas on this subject too.