Analysing the voice of a poem is somewhat similar to analysing the narrator of a work of fiction. The first step is determining who is speaking and the point of view.
For point of view, you need to loom at grammatical person first, which can be determined by pronoun use:
1st person singular I, plural we
2nd person singular and plural you
3rd person singular he/she/it, plural they
Next, think about the narrative persona as a distinct fictional device (don`t assume the 'I' of a poem is a biographical reference to the poet). What sort of clues do you get from the poem? Does the title tell you something (e.g. the title 'Tithonus' suggests that Tennyson's poem is spoken in the voice of the mythical character Tithonus). Next look at the tone or attitude of the poem, e.g. the monk`s criticisms of Father Lawrence in Browning`s Soliloquy of the Spanish Cloister` give one a sense of a bitter voice verging on insanity. Look also at the diction and sound patterns -- e.g. the tone and rhythm of 'My Papa’s Waltz' by Theodore Roethke create an innocent childlike voice.