How do I analyse an unseen poem?

It's important to begin by reading the poem through not just once, but a few times. This will help you become familiar with its form and content, and ensure that you haven't missed out or misinterpreted any key information. That's the thing with poems: they're not always easy to understand on the first read! Once you have an understanding of the poem's theme and content, you can go on to see how this is reflected in the form and language.
Search the text for any poetic techniques that may stand out, such as alliteration, onomatopoeia or metaphors. It is also important analyse the form and structure - make notes on the rhythm and rhyme as well as any cases of caesura or enjambment. In each instance, try to understand why the poet has used this technique and how it is effective. This is important when it comes to the structure of your essay, where you should include your Point, Example and Explanation: what is the poem doing, where does this happen, and how or why does this happen.