I would focus on the character of Blanche, since the play is about her downfall. My reaction is that she is defeated from the very beginning. She does not approve of Stella's honky-tonk environment, and she especially disapproves of Stella's husband. They dislike each other from the beginning. But the contest between the protagonist (Blanche) and the antagonist (Stanley) over the MacGuffin (Stella) is unequal. Blanche has no weapons but her flirtatiousness and refined manners. Stella makes it clear that she is crazy about Stanley (for whatever reason) and wouldn't consider leaving him, as Blanche urges her to do. On top of being so strongly attached to Stanley, Stella is expecting a baby and will become even more dependent on him. Stanley is actually long-suffering. He allows Blanche to stay in their two-bedroom apartment for five months, during which time he provides all her food and liquor. For a violent man, he shows extraordinary patience and tolerance. The approaching birth of Stella's baby is like a ticking time bomb. If there is no room for Blanche now, there will be less when the baby is brought home. The contest between Blanche and Stanley is a no-win for Blanche from the beginning. But Tennessee William has given her a notorious background in her hometown. She not only behaved like a prostitute, but she was fired for seducing underage male pupils. This seems to make Stanley's victory too easy. He could have kicked her out without having all that information about her past behavior to use against her. Mitch could have rejected her just by finding out that she was older than she pretended to be. He didn't need to be informed about her really outrageous past conduct.
If it is overwhelming for you to react to the entire play, perhaps focus on your reaction to one aspect that is carried throughout the entire play. For instance, you could describe one character and how you felt about his/her actions throughout the play. Or, if you are writing about production aspects from viewing the play on stage, you could react to some particular aspects of the production such as set, costume, or lighting. Really, how specific you get in your reaction depends on the length requirement and context of the paper.
You have some excellent suggestions from the preceding posts. One of the biggest issues for a student writing a reaction paper is organizing your thoughts. During the prewriting stage, if you have a "bank" of notes describing your reactions it is very helpful. Another way to approach the paper is to select a character, event, or theme that struck you during your reading, and make that your topic. You can then describe your reaction and thoughts in reference to the character of Stanley Kowalski, for example, and Stanley becomes the focus for your draft.
I agree with #2 - a brilliant way to start this assignment would be to read the play and keep a journal of your reactions and emotions at each stage of reading. Were you surprised by anything? Could you see it coming? What scenes affected you emotionally? How and why? These kind of questions will help you in defining your own personal response to this excellent play. Good luck!
Since a response, or reaction, paper is written to help the reader better understand how he feels about a literary work, the focus is on the reader's own personal feelings. Thus it is advisable that the reader jot down his reactions and thoughts as he reads; then, he can review them and find common threads of personal ideas that can be organized into an essay.
The response essay is unlike others in that it is subjective and the writer uses the first person point of view. Thus, the thesis statement presents the readers opinion of the literary work or of a certain aspect of the work. For instance, the reader of Tennessee Williams's A Streetcar Named Desire could write a reaction essay about the employment of Expressionism by Williams. Or, it could have a reaction to the effectiveness of the use of symbolism and imagery, or the character Tom as narrator as well.
So, peruse the notes that you have taken, think about your strongest reactions after you finished reading, and formulate them into a single collective idea/opinion that you can use as the focus of your paper/essay. At the same time that you form a collective idea, find supporting details from the play that will support this idea. See the sites below for more help on writing.
You could focus on how you feel about the exposition, the crisis, the climax, or the falling action, and the reasons why you feel that way according to the story. A theme might be easy enough for you to come up with, and if you have a few reason why, those become your controlling ideas.