How do I write an essay about "The Love Song of J. Alfred Prufrock" by T.S. Eliot?

You could focus on the examination of the central character of the poem. The poem's importance lies in the fact that Eliot depicts a prototypical man of his time by presenting us with the character of Alfred Prufrock. This character, who is the epitome of modern man, is emotionally paralyzed, hopeless, alienated, lonely, indecisive and awkward. He is the man of contradictions; he demonstrates a desire to change his life for the better, yet he is unable to do it because he feels he is "not Prince Hamlet, nor was meant to be." He believes that he is not a hero of any sort; instead, it is implied that he is the victim of the time he is in, the time of moral decay and emotional paralysis, which Eliot wanted to describe to us.

Alfred Prufrock wants to take a walk with an unspecified "you" through the tawdry streets (presumably London streets):

Let us go, through certain half-deserted streets,

The muttering retreats

Of restless nights in one-night cheap hotels

And sawdust restaurants with oyster-shells:

Streets that follow like a tedious argument

Of insidious intent...

The streets evoke images of moral decay, squalor and wickedness. As the poem continues, we become aware that Alfred Prufrock lives in the world where scenes of superficiality and banality are predominant. For example, in his mind he views women talking about the famous Renaissance painter Michelangelo. This scene is replayed in his mind, which suggests that people in Prufrock's world engage themselves in repetitive and monotonous actions, exemplified by women's meaningless chatter about art.

Prufrock never finds the right time to deal with his biggest concern -- he is terrified of talking to his love interest because his mind is fixed on too many preconceptions about the possibility of failure and how other women could see him:

They will say: “How his hair is growing thin!”)

My morning coat, my collar mounting firmly to the chin,

My necktie rich and modest, but asserted by a simple pin —

(They will say: “But how his arms and legs are thin!”).

Alfred suggests that he is already labeled and classified in the minds of other women, so he believes that his effort to make the next move would amount to nothing more than rejection:

 And would it have been worth it, after all...

If one, settling a pillow by her head

               Should say: “That is not what I meant at all;

               That is not it, at all.”

The poem is a depiction of the emotional paralysis, banality, and hopelessness of the time Eliot lived in. Eliot's modern man is disheartened, incomplete, and unfulfilled. So, we may view this poem as Eliot's attempt to criticize the world he lived in and encourage change.