Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Exposition (Initial Situation)
It's a Period Piece!
Austin has come to his mother's house to focus on his next big writing project, a period piece about love. He's been talking with a Hollywood producer about the idea, and it looks like he has a good shot of getting this idea sold. Maybe that would all go smoothly if Austin's older brother Lee hadn't also shown up at their mom's house. The brothers haven't seen much of each other over the years, and they seem to be very different people. While Austin spends his time with his wife, kids, and writing, Lee prefers disappearing into the desert, stealing things, and dog fighting.
Rising Action (Conflict, Complication)
Trading Places
While there's a level of conflict between the two brothers from the start, things start to get bad when Hollywood producer Saul Kimmer shows up. He's excited about Austin's script idea, and he wants to move forward and get some money to turn it into a movie, but then Lee comes home and mixes things up. Lee convinces Saul to hit the links and go golfing the next day. It turns out Lee's got himself an idea for a movie—a "true-to-life Western" (1.3.162).
That night, Austin helps Lee put together an outline for his movie idea. After Lee meets with Saul on the golf course, he comes home to tell Austin that Saul is going ahead with his Western and dumping Austin's period piece. This news sends Austin into a bit of a rage. Even though Lee wants Austin to write the script, Austin refuses. As Lee starts to try to write the script on his own, Austin decides he will start stealing things just like Lee does. Pretty soon, the house is full of ripped off toasters that Austin stole from neighborhood houses, a battered typewriter, and two sweaty and drunk brothers who are quickly losing any grip on sanity.
Climax (Crisis, Turning Point)
Brother Against Brother
Remember at the beginning of the play when Austin was sort of a reserved writer just trying to write a period piece about love? Yeah, that's not the case anymore. Austin has reached the point where he is ready to give up his life and head out to the desert if Lee will just take him. Lee, still struggling to write anything, tells Austin that he will take him to the desert once Austin helps him write the script. The deal seems like a good one, and the two crazed brothers start trying to make their way through a script.
At this point, it's important to realize that the place has pretty much descended into chaos. Sure, sometimes your bedroom gets messy, but chances are it doesn't look like a tornado ripped through it. Well, that's how the house looks now. Stolen toasters are thrown all around the kitchen, burnt toast is on the floor, the typewriter is bashed into pieces, the phone has been ripped out of the wall, all the plants are dead, and the brothers are kind of wallowing in their own filth.
Luckily, their mom shows up to set things right.
Except that doesn't really happen.
When Mom shows up, all hell breaks loose. Lee tells their mom that he's heading out to the desert, and he makes it clear that Austin will not be coming. Austin will not take this lying down. In fact, he's going to fight about it. Austin attacks Lee, and the two start to fight like wild animals as their mom calmly says things like "You'll have to stop fighting in the house. There's plenty of room outside to fight" (2.9.256-258).
In the end (with a little help from a phone cord), Austin chokes Lee out. It looks like Lee is dead.
Falling Action
The Dead Shall Rise
Falling action moves fast in this one. Austin tries to see if his brother is alive. It really looks like Lee is dead. Austin drops his weapon of choice (the phone cord) and moves to the door as if to leave. Not so fast, son! Lee leaps up, "blocking AUSTIN'S escape" (2.9.340).
Resolution (Denouement)
The Lone Coyote
The two brothers stare at each other close to the door, still but waiting to see who will make the next move. Then things get a little weird. Shepard lays out the closing image of the play like this:
They square off to each other, keeping a distance between them. Pause, a single coyote heard in distance, lights fade softy into moonlight, the figures of the brothers now appear to be caught in a vast desert-like landscape […] lights go slowly to black as the after-image of the brothers pulses in the dark, coyote fades. (2.9.340-346)