First, I would read the poem as if I were reading it for enjoyment. I would simply try to understand its basic meaning and enjoy its images, rhyme, rhythm, etc.
Next, I would re-read the poem and take notes about its content. What is its theme or message? What are its prinicipal images? Is there a narrative? If so, what happens, and why?
Then, I would read the poem a third time and take notes about its form. Does it rhyme? If so, what is its rhyme pattern? Do the lines all have the same (or approximately the same) number of syllables? Is there a clear rhythmic pattern, such as iambic or dactylic? Does each stanza discuss a specific point, leading to some conclusion? Or is this poem an example of free verse, with no set rhythm, rhyme, or structure?
When writing the essay, I would probably start with the content. Later, I would identify the various forms and techniques that are used. Finally, I would attempt to show how the form is appropriate to the content.