Explain how the poem expresses a general sense of despair. How do figures of speech convey tone?
Eliot's poem is the dialogue of a man with himself about whether to ask a woman to marry him. His self-esteem is so low and his self-confidence so lacking that he doesn't even attempt to do what he would like to do because he just knows he will fail. The writer of the essay "Understanding the Love Song of J. Alfred Prufrock" calls him a "trimmer":
Trimmers were those souls in Dante's Inferno who were condemned to the vestibule of hell because they had never really lived, although they were supposedly alive; but they never really did enough evil to be sentenced to hell, and they never did enough good while they were alive to get to purgatory to start their way up to heaven. The Trimmers were lifeless, spiritless, mindless people.
The most prevalent literary device, or figure of speech, used in the poem is allusion. He compares himself to John the Baptist, Michelangelo, Lazarus, and Hamlet. Berryman's essay on Prufrock's dilemma (see the link below) notes that "it was women who got the Baptist beheaded. We might phrase the meaning as: I announce no significant time to come, I am the forerunner of (not children, not a Saviour) nothing."
It is interesting that Eliot himself had a stormy relationship with his wife, Vivienne. She suffered from a mental illness and eventually was institutionalized. A movie based on their lives, "Tom and Viv," speculates that he wrote his epic poem The Wasteland in the midst of this tumultuous relationship.
I agree with the above answer and would like to emphasize one point. We are seeing the burden of awareness in Prufrock. He is completely aware that his best (relative term here) days are behind him. He is past any rationalization that things are any other way. His potency in all aspects is waning and this seems to grip him with fear. He foresees a life where everyday he will feel respected less, admired less, desired less, mocked more, ignored more, exposed more and misunderstood more.
The poem begins with a testimony regarding the torment of hell. For Prufrock, his hell is his life, as it dwindles before him into a lonely, weak shell.
I would want to add that I don't necessarily think J. Alfred Prufrock has had that great a life up to now. He is a man who measures his life in "coffee spoons" for goodness sakes. When he contemplates the future, it is clear that his life, as bad as it is, can only get worse. The figurative langauge that is used only reinforces the impression of an isolated, self-obsessed and somewhat narcissistic figure who can't find the courage to truly live and feels life slipping away from him too quickly.