Answer:
First be sure of your definition of a poem. If you accept, for example, that it is "the spontaneous overflow of powerful feelings," then ask yourself if you can zoom in on that author's feeling by reading the poem, preferably aloud. What did you feel or where did you imagine yourself while reading the poem.
Examine the context of the poem by answering the question "What was the author's purpose or goal in writing this poem? Is he/she playing with words, honoring a friend, admiring nature, or celebrating history etc.? Is it musical?
Does it have an effect on me? Does it offer advice or have a philosophy? Or does it simply entertain?
Then using a glossary of poetry terms we can tell how the author achieved his/her goal. How many stanzas, verses in each, rhyme; what kind of rhyme?
Does it fit into a literary movement or type of poetry. Does it have a unique structure or a classical structure? Can you spot examples of metaphors and
simile? Is the language violent enough to prose to be called poetry?
Does it imitate any previous poem or set a standard for other poems that followed?. What were they?