Read the poem carefully, asking yourself the same question twice: "What is the poem about?" The first time you ask it, read for exposition---the who, what, where and when of the poem. The second time you ask it, read for theme, or extended metaphor---is this a poem of regret? Of grief? Of wonder? Make notes.
Decide on a thesis. A thesis is an arguable statement and should always be stated in one clear sentence. For a poetry analysis, your thesis might argue, for example, that the poem's extended metaphor has a certain meaning. Or you might argue that the poet's life circumstances affect the meaning of the poem, or perhaps you believe that a repeated word or image in the poem, called a motif, has a certain symbolic meaning.
Open the essay with a brief paragraph that mentions the name of the poet as well as the poem and its theme. Also, introduce some basic information that led you to your thesis, and make your thesis statement in the last sentence. For example, if you are going to argue that Carl Sandburg's "Chicago" is a love poem to the city, you might first mention that he seems to be praising the city, even though the poem is largely comprised of lists of the city's unsavory and dirty characteristics. Essays about poetry are analytical arguments, according to Purdue University's Online Writing Lab, and as such, they will always state a thesis, which is an arguable idea.
Discuss passages from the poem that support your thesis in a series of paragraphs that flow logically from one to the next. Use one or more direct quotations from the poem to develop each paragraph, and explain how each quotation supports your argument.
Mention literary devices---such as symbols, personification and irony---throughout the body of the essay because it is relevant to do so, suggests Purdue University's Online Writing Lab. This way you demonstrate basic subject knowledge of poetics.
Devote some text in each paragraph to discussing counterpoints, if there are any. For example, if a line can be interpreted in more than one way---such as the line, "City of the Big Shoulders" in Carl Sandburg's "Chicago"---address all of the readings of the line. You may say that one reading is a misinterpretation and explain why, or you may admit that more than one reading might be correct and that they all enrich the poem's meaning. For example, "City of the Big Shoulders" may symbolize three different items: the urban skyline of a growing city, the hard-working laborers who inhabit it and the bullying nature of a rough big city.
Conclude the essay with a final summary, which might include a powerful quotation from the poem that makes your point. Or it may echo the introduction you wrote or both.