Read the poem aloud. Poetry revels in sounds. Thus, you need to hear it with your ears. Also, many poems are built on rhythmic patterns, and this rhythm will more likely come alive for you when you hear it.
Clarify or define unclear words. Many people are discouraged by the word choice -- diction -- of poetry, and wary because they fear they won't understand it because they will come across unfamiliar words. Keep a dictionary handy.
Try to discern the artistic features of a poem. Here are features to look for: words or phrases that are repeated; patterns of rhyme or sound. Determine the type of poem: Is it a sonnet, ode, epic, free verse?
Look into the historical background of the poem and poet. Who was the author? What do we know about him? When did he live? What is the occasion for the poem? Who was the poem written to or for?
Pay attention to metaphors. What are the metaphors (A IS B) and similes (A IS LIKE B), and what is the point of comparison (How A is B, or is like B)? Metaphors can help us understand poetry by engaging us on an emotional level.