In this poem, Prufrock is speaking to an unidentified male companion (according to Eliot himself) but it also seems like Prufrock is speaking to himself as if in soliloquy or an interior monologue. The epigraph is from Dante's Inferno. In this context, a character in the Inferno tells his story to the poet believing that it will never be repeated. Whether Prufrock speaks (to a friend, to himself, or hypothetically to a woman), we can intuit from this epigraphy that Prufrock speaks with the same assumption: that this will never be repeated. Therefore he is free to expound on his feelings.
Prufrock begins by procrastinating. He speaks of a room where "the women come and go." He notes that "there will be time" to go and meet some woman/women:
Time for you and time for me,
And time yet for a hundred indecisions,
And for a hundred visions and revisions,
Before the taking of a toast and tea.
There will be time for having toast and tea with women. There will even be time for more indecision prior to any such meeting. He continues with this procrastination in the subsequent lines. Prufrock is consumed with self-doubt, thinking that he will not play the correct role required of him in social situations with women. However, his desire might override his doubts. "Is it perfume from a dress / That makes me so digress?" Is it a woman's allure that makes him digress from his self-deprecations?
Prufrock is so conflicted by his desire and his fear of rejection that he exaggerates the state to which he thinks he must bring himself in order to have the courage to meet with this woman. He thinks he would be Lazarus, back from the dead, "Come back to tell you all," and here the "you" indicates the woman. She supposedly would reply "That is not what I meant at all." In other words, she merely wants a social meeting. Conflicted with desire and fear, Prufrock thinks he needs some profound truth in order to override his fear of making small talk and being socially elegant. In lines 100-110, Prufrock wonders if his effort would be worth the possibility of rejection. Either he will fail to express himself properly or she will not see the depth of what he is trying to say. "It is impossible to say just what I mean!"
Prufrock is divided between his inner self and the self he projects onto the social world. In the end, he compares women to mermaids, something exotic and alluring. However, since he can not bring himself to express his inner self in the social world, he does not think that the mermaids (or their real counterpart, women) will sing/talk to him. He deeply desires the company of a woman but he can not seem to find a connection between the sense of his divided, inner/social self. Until he wakes up from this self-division, he can't help but think of women (or the social world of relationships) as something exotic and alluring but beyond his grasp or understanding: like a mermaid.