I remember the first time I read this poem I felt completely lost and didn't understand what was going on, so you are not alone in feeling confused by this poem! I have included a few links below to the relevant study guide section on enotes to help you negotiate the poem, but I will also give you a summary here to hopefully give you a few "hooks" that you can use to understand the poem and what Eliot is trying to achieve.
Firstly, let us observe that this poem is a dramatic monologue, in that it is a poem where one character is speaking to one or more listeners. Thus it is that the words of the poem are spoken by the J. Alfred Prufrock of the title. The poem therefore gives us access to his mind and character, and a vitally important question to consider is what the poem tells us about him, and what kind of man he is.
As it begins, it is obvious that as Alfred Prufrock is walking, he is thinking about asking a question, but he cannot bring himself to ask it. He remembers roaming through deserted streets. He shows himself to be concerned and obsessed about his appearance, worrying about what others will think of him. He draws attention to his own physical deficiencies, such as his baldness. He expresses an intense desire to have the courage that he needs to assert himself, and he clearly longs for romantic love, but at the same time his fear of being made fun of or being misunderstood acts as a profound barrier to his interactions with others. The poem ends with the crushing realisation that his timidity and fear of failure will mean he will never acheive his dreams.
In short, he is a man who is obsessed with his own insecurities and what he thinks others might think and might say about him. Note one of the most famous lines from the poem:
Do I dare
Disturb the universe?
In a minute there is time
For decisions and revisions which a minute will reverse.
Resoundingly, Alfred Prufrock does not dare to disturb the universe, and his focus is always on the impact of "decisions and revisions" and what the effect of various actions could be. He is paralysed by indecision and his own personal hang-ups.