Essays analyzing poems usually cover author, genre, form and content.
Begin by briefly summarizing salient facts about the author, including dates, most important works, whether the author was part of a major literary movement, and any facts pertinent to the composition of the poem (e.g. Coleridge's account of the composition of Kubla Khan, Tennyson's intending "Crossing the Bar" to be placed last in all editions of his work as an epitaph).
You should specify the genre of the poem -- whether it is lyric, epic, satire, ballad, etc.
Next, analyze the form. You might scan the poem and describe its metrical structure and any important or characteristic variations (e.g. "Written in regular heroic couplets with occasional isometrical substitutions" or "iambic pentameter open quatrains with frequent anapestic variations). Next, look at figures of speech, levels of diction, etc.
Finally, cover content including voice, point of view, themes, symbols, intertextual allusions, etc.
Like how I analyzed the poem I was working on I would find:
1) What the poem is about?
2) Who is it from and for who?(Maybe it's not just for who but about what) Example: Donald B. was writing about how much he misses his journey to Spain
3) Does it have a structure? Then Identify what type of structure it has. For example a Sonnet with 3 quatrains (3 groups of 4 lines talking about the Main idea, Dilemma then a more in-depth dilemma) then a couplet (the TWO lines that summarizes a conclusion)?
4) Does it have the same number of syllable on each line keeping consistency? Identify what they are called. For example Iambic Pentameter = 10 syllables or beat of each line (applies with Sonnets)
5) What is the poem's rhyme scheme? List them with A,B,C,D and so on if the lines rhyme with another (watch out with 'Half Rhymes' where only the last syllables rhyme. They don't count, only full word rhymes do.) Eg. A,B,B,A,C,D,D,C,E,F,F,E,G,G
6) is there the same number of syllables on each line consistently? If there is one or two odd ones out then try and figure why they are like that. Is it to emphasize maybe?
Here are just a few, You can write a lot about each point in more depth. But to structure it all in a formal manner, like a report, I'm not quite sure how to do so.
I hope this helps.