There are two ways to analyze a poem. One, stylistically and the other, a generally. Remember few points to analyze a poem. Analysis is only a interpretation of a work. Firstly, read the poem thoroughly thrice, then ask yourself these questions:
What is the poem about? Who is the speaker? Is the speaker different form the poet?(Remember if there is a reference made to the poet as a seperate entity, then the poet & speaker are different), Who is the speaker speaking to? What is the situation? What is the tone of the poem? Is it grave, refleactive, happy, sad, thoughtful, What kind of poem is it?(ballad, sonnet, epic, etc.) How many lines is it, are there any paragraphs, Is t wriiten in free verse or there is a rhyme pattern? Look into the rhyme scheme, meter(Iambic pentameter, tetrameter, etc).
Then, analyse the grammar part. Bring out the figures of speech, imagery, connotation, denotation, parts of speech(effect of nouns, verbs, repetitions, etc). Talk about the syntax(sentence sructure), whwther the sentences are long, short, easy, difficult, paraphrasing.
Finally conclude by talking about the overall effect of the poem on the reader or you. All the best. Hope this helped :)