Look at the poet's other work. Scan them and look for familiar themes and vocabulary. Read the poet's biography and note how his or her life has impacted the poem. Most poets use their life as an inspiration for most of their poetry.
Deconstruct the poem. Take the poem apart, piece-by-piece, looking at different elements separately. Think about who's narrating the poem, the situation they're describing and their attitude. Look at the visual images and the poem's theme, or the main issue that it addresses.
Study the language and syntax. Check the poem for similes, metaphors and personification as well as irony, hyperbole, allusion, puns and other rhetorical language. Note how these devices further the poem's theme and the narrator's beliefs and emotions.
Explain the imagery in the poem. Poetic images can be concrete or realistic or they can be abstract and evoke certain feelings. Tie the images to the overall theme of the poem.
Analyze the syntax and format. Many modern poets use free verse, but formal poetry like haiku, sonnets and quatrains continue to be popular. Some poetic forms have a rhyme scheme similar to a song, like the villanelle.
Tie all these elements together. Explain how they relate to one another to form the meaning of the poems. Many poems can have more than one interpreted meaning. Cover the various meanings in your report or thesis.