If you are asked to analyze a poem, a good place to begin would be to figure out what you believe the purpose of the poem (or excerpt) is and how the poem achieves that purpose. What subject does the poem take, and what is the poem's position on that subject? First, seek to figure this out. Next, you should also consider any poetic devices (e.g., personification, metaphors and similes, symbols, sound devices like alliteration or onomatopoeia, irony, paradox, etc.) the poet uses to help convey the poem's meaning or purpose. Then, you can use a template like the following to write a thesis statement (main claim) about the poem: The poem ["Poem's Title"], by [author's first and last name], conveys the idea that [insert what you believe to be the poem's purpose or meaning here] through the use of [list poetic devices here]. From there, you can begin to explain how the poet's use of the specific poetic devices you've identified in your thesis work to achieve the poem's meaning.
For example, you might say, The poem "Much Madness is divinest Sense," by Emily Dickinson, conveys the idea that the majority is generally wrong, and so those who follow the majority are crazy, through the use of paradox and metaphor. The paradox—that madness is sensible (line 1) and that sense is "the starkest Madness" (3)—is explained by the reference to a "discerning Eye" (2). Only a person who is discerning, perceptive, will see that "Assent[ing]" to the majority opinion is actually "Madness," while "Demur[ring]" is the smart and sane thing to do (6, 3, 7). If a person disagrees with the majority, then the majority says that this person is "straightaway dangerous" and "handle[s] [them] with a Chain" (7, 8). In other words, the dissenter will be treated like a crazy person that must be locked up, as though they are criminally insane and must be restrained. This metaphor helps us to understand how the majority sees anyone who dares to disagree.