I always found it useful to use the following structure when reading a piece of poetry for the first time, and even after that:
Language - What devices are used and why? For example, does the poet use alliteration to stress a certain point?
Attitude - How do you think that the poet feels about the subject that they are writing about? Do they react positively or negatively to their chosen subject?
Tone - How do they convey their attitude? For example, they may use sombre vocabulary, or try to create a cheerful mood.
Intention - Why did the poet write the poem? It may have been out of anger, bliss or other emotions.
Narrative - What is the poem about? Do you think there is any deeper meaning to the poem other than what is on the surface?
Style - How is the poem written / laid out? It may flow nicely, or the poet may have made it jerky and awkward to read. Why do you think they did this?
This spells LATINS, for an easier way of remembering it. The order can be switched around depending on personal style.