Read the poem carefully. Paraphrase the words, and try to decipher what the author is trying to convey. Poems might not have a story or set of events, but rather a conveyance of mood or emotion. Poems can also be used to make a point about things like politics, religion, relationships or the world around us. The more you can understand the poem, the easier it will be to write the thesis for your paper.
Figure out how you want to approach your analysis paper. Your instructor might have already answered this for you with your assignment. For example, your assignment might be to analyze the meaning of the poem, the symbolism in the poem or the use of language in general. If you were not given specific assignment instructors, choose an aspect of the poem to analyze in your paper.
Interpret the meaning of the poem in regards to the type of analysis you chose as best you can. For example, if a poem seems to be discussing springtime but is really conveying a point about the destruction of the environment by human beings, pull out all the language that helped you draw this conclusion. You will use this language in your paper to help you analyze the poem's true meaning.
Incorporate your analysis into a cohesive thesis statement. The thesis statement should be the point you're making about the poem or the interpretation that you have made. Using the above example, your thesis for the poetry analysis paper might be something like, "The author uses metaphors, connotative language and disparaging imagery to convey a strong message of environmental destruction." The rest of your analysis paper will give examples from the text that helped you draw this conclusion.
Alter your thesis statement as you write your essay. For example, you might discover that the author uses more similes than metaphors, which means you would change the wording of the above thesis statement to "The author uses similes, connotative language and disparaging imagery to convey a strong message of environmental destruction."