How should a poem be analysed?

The formulaic method I recommend is SPECS and SLIMS. 

Subject:  What is the event or experience the poem decribes/records?

Purpose: What message does the poet try to communicate? Why did they write the poem?

Emotion: What is the mood of the poem? How does this change, and what emotions does the poet evoke in the reader?

Craftmanship: How does the poet achieve this effect? What poetic techniques have been employed? See SLIMS

Summary: What is the impact of the poem and does it achive its purpose? 

Structure: How is the poem structured? Is there a conventional structure such as a sonnet? Does it have stanzas with a regular number of lines such as quatrains, sestets?

Language: What langauage features are used? Is this appropriate to the theme conveyed - colloquial dialect etc.?

Imagery: What is the effect of these devices (similies, metaphors, imagery, symbolism, personification)?

Movement: What is the poem's rhythm - is it regular or irregular? Are there examples of enjambement which add to the pace of the poem?

Sounds: Are aural features used: onomatpoeia, alliteration, assonance, sibilance? Does the poem rhyme: if so/not what is the effect?