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)
Older Brothers are a Real Pain
The Duchess is an aristocratic widow secretly looking to remarry, but her brothers Ferdinand and the Cardinal are hell-bent on her staying single. To keep her in line, they insert their spy, Bosola, into her court as her employee. So far, things are a little strange (solo Duchess, obsessive brothers, spies, etc.), but, given the political and family ties at play, basically par the course.
Rising Action (Conflict, Complication)
Mawwige, That Bwessed Awwangement
The Duchess secretly woos and marries her steward Antonio, defying both her brothers and her society by marrying her social inferior. They actually have a really happy marriage, but what with the subsequent pregnancies and having a spy in her court, their secret eventually gets out. The Duchess knows she's messing with social norms and her brothers, but figures (optimistically and incorrectly) that she can keep a lid on the situation.
Climax (Crisis, Turning Point)
No, Really, Older Brothers Suck
The brothers, having found out about the Duchess's marriage and kids, make it their mission to destroy the new family. The family splits up, and Ferdinand successfully captures, imprisons, and then executes the Duchess, two of her three children, and her maid Cariola. After this, stuff goes from crazy to crazier, and the plot spirals into an escalating series of plots, betrayals, and murders.
Falling Action
Werewolves of London (Naples, Actually)
Bosola, horrified at how everything's turned out, vows to save Antonio and avenge the Duchess. Ferdinand, after having the Duchess killed, goes crazy, and falls victim to lycanthropia (thinks he's a werewolf). Antonio, naively believing that he can resolve everything by just talking it out with the Cardinal, goes to surprise him his castle in Naples, only to be accidentally killed by Bosola upon his arrival. Don't be fooled by the "falling" part of "falling action"—it doesn't mean that things are "winding down," it means that this is the stuff that comes after the climactic event of the Duchess's execution.
Resolution (Denouement)
Nobody Can Catch a Break in This Play
Bosola successfully kills Ferdinand and the Cardinal, but is himself mortally wounded in the process. After he dies, the only surviving son of the Duchess and Antonio is brought in by Antonio's BFF Delio, who intends to instate the boy in his mother's political title.