For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
Prince Fabrizio sits down with his family for dinner. He's in ill humor because he knows his status as a royal prince is going to disappear once foreign troops invade his country and unify Sicily with Italy. He visits his mistress to get his mind off things, but it doesn't help for long. He feels old and tired and realizes that all things must pass… including himself. His family's has royal status for centuries, but now someone else is going to be powerful.
Act II
Fabrizio and his family travel to their country estate in Donnafugata. While there, Fabrizio's nephew Tancredi falls in love with a local girl and gets engaged to her. Foreign troops take control of Sicily and Fabrizio is offered a role as senator in the new government. He's too proud to go from Prince to senator, though. Besides, he no longer has the energy to care about holding power. He's willing to just live out the rest of his life in boredom and despair. Now that sounds like a depressing plan.
Act III
Sixteen years after the unification of Italy, Prince Fabrizio dies of a stroke. In his final moments, he sees the figure of Venus appear at the edge of his bed. This is the woman he's been waiting for his entire life, and it looks like only in the moment of death is he able to embrace her. We know that she's just a figment of his imagination, but she still represents the peacefulness that Fabrizio has wished for his entire life.
After Fabrizio's death, we flash forward another twenty-two years. Now Fabrizio's daughters are also very old. None of them have had children, so the royal Salina line will end once they're dead. A religious official inspects their family chapel and removes a bunch of phony old religious artifacts that the sisters thought were real. In the book's final moments, the sister Concetta decides to throw out their family dog, Bendicò, who's been dead and stuffed since her father's time. Throwing it out marks the end of the book and the end of the Salina family.