A good start when analyzing poetry is a simple visual and auditory analysis of the poem. The University of Texas at Austin Undergraduate Writing Center's guide to analyzing poetry suggests reading the poem out loud several times and making notes of anything interesting. Print out a copy of the poem and take notes on it. Look over the printed poem and make note of how the poem is structured and how it appears visually on the page, including stanza length and form.
Close reading is a way to analyze a poem that relies on paying close attention to the poem's form and word choice. Purdue's Online Writing Lab recommends that a reader take note of aspects of the poem's form like line length, rhyme scheme and word repetition. It's also important to analyze what figurative language is used in the poem. Look for metaphors, similes, alliteration and imagery.
Scansion, the act of determining the rhyme scheme of a poem, is another method. The Purdue Online Writing Lab's guide to meter and scansion defines it as the act of determining what syllables in a line of poetry are stressed or unstressed and then determining what pattern the syllables in a line of poetry then create. Syllables in any word are either accented or unaccented meaning the syllables are either stressed or unstressed when the word is spoken. A stressed syllable is accented while an unstressed syllable is unaccented and receives less emphasis when spoken.
Poetry also can be analyzed by looking at its genre and cultural context. The University of Texas at Austin Undergraduate Writing Center's guide to analyzing poetry suggests that a reader consider when the poem was written, what the important social and political issues were when it was written, and whether the poem's form and genre are consistent with the literary conventions of its era.