The reading is Michael Cunningham's brutal, beautiful "White Angel"
This story of childhood, drugs and tragedy in late 1960s Ohio became a chapter in the novel A Home at the End of the World, which was made into this movie.
In this story, pay special attention to the dialogue, and particularly what goes unsaid—the secrets the characters keep from one another. As John Garnder says in his famous dialogue exercise (see below), pay attention to what makes the dialogue "crackle with feelings not directly expressed."
For example, look at the conversation between the narrator and his mother, when he comes back into the house after seeing his brother and brother's girlfriend in the graveyard. In the linked pdf this is towards the bottom of page 31. What secrets are being kept here, exactly?
There's the obvious one: the narrator lies and says his brother Carleton is not doing drugs. But I would argue this obvious one is not the main secret—it's not even really a secret at all. "Lately police cars have been browsing our house like sharks," the narrator says, and his mother has noticed. She knows "something's going on." She tries to whack the answer out of the narrator with the vegetable brush and fails, but she doesn't really need him to give her the information: she already has it.
So what are the unsaid things that make this dialogue crackle? I would argue that not only are they far from simple and obvious—things like drugs, or a lover in the bedroom—they are so big and complex that they can't even be put into words: the feeling the narrator gets when Carleton sees him and winks at him in the graveyard; the narrator's preadolescent, absolute allegiance to his doomed brother that divides him forever from his parents, a division that repeats itself in every generation but which, in the late 1960s, and in this specific family, has its own terrifying and tragic flavor. I think the story as a whole answers the question "what are the unsaid things?" and there isn't really a way to reduce the answer to anything smaller than that. You feel it in every beat of the story, every interaction between the characters.
This is, in part, a story about two boys sharing a house with their parents but living in a completely different universe. There's a tragic climax, but the story is suffused with tragedy from the first page: it lies in the fact that there are so many secrets, so impossible to communicate that they form a vast gulf that separates all the characters from one another—a gulf that, in the end, seems to widen to infinity.
And here is the John Gardner exercise, one of my favorites, from his classic The Art of Fiction:
Write a dialogue in which each of the two characters has a secret. Do not reveal the secret but make the reader intuit it. For example, the dialogue might be between a husband, who has just lost his job and hasn't worked up the courage to tell his wife, and his wife, who has a lover in the bedroom. Purpose: to give two characters individual ways of speaking, and to make dialogue crackle with feelings not directly expressed. Remember that in dialogue, as a general rule, every pause must somehow be shown, either by narration (for example, "she paused") or by some gesture or other break that shows the pause. And remember that gesture is a part of all real dialogue. Sometimes, for instance, we look away instead of answering.
I recommend setting your timer for ten minutes and diving right in. Remember this is an exercise: you can throw away the result if you don't like it! (But you might be surprised.)
If you're already working on a story, think about the next scene you need to write, and use this to do it. If you don't have anything going right now, start from scratch. Need ideas? Here's a list of characters and here are some problems you can give them. Have fun!