How do you analyse a poem

Read the poem twice, and a third time aloud. Highlight any language that stands out to you - whether for its tone, technique, imagery, clarity or ambiguity (etc.) Write down your ideas and questions at the bottom of the page. All questions are good, even 'why wouldn't he rhyme that stanza' or 'why would she describe it like that'. Read the poem aloud, noting the rhythm and length. Pay attention to where you may stumble over words, or where the poem is particularly pleasing to read.
Read the question and read it again. Highlight the key words, noting what the question is asking you to hone in on. Read the poem again with the question in mind, thinking about how it relates to your idea of the poem. Use these ideas as a basis to build your argument.