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)
Inherited Finances—the Ties that Bind
Lady Britomart comes from a noble family, but she doesn't have much of her own money to dispense to her children—which is unfortunate, since it means she has to depend on her estranged husband, Andrew Undershaft.
Her daughters are about to get married to men who aren't likely to be able to support them in the immediate future, so she's gotten in touch with Andrew in the hopes of squeezing him for some more cash.
The play opens with her powwowing with her son, Stephen, about the family's financial difficulties, and she basically bullies him into advising her to ask Andrew for help—which is fortunate, since she had already invited Andrew over that night. They also discuss the fact that Andrew plans to cut Stephen out as the heir to the family business per a family tradition of passing control of the firm to a foundling. The tradition is what caused the breach between Undershaft and Lady Brit in the first place.
Rising Action (Conflict, Complication)
Getting the Undershaft
When Andrew Undershaft arrives and sees his children for the first time in years and years, it's a little awkward—he can't seem to remember who is who, or even how many children he actually has—but soon Sarah and Barbara (and their fiancés) are pretty well charmed. Barbara and Andrew banter back and forth about their very different professions—Barbara's job is to save souls and feed the poor, while Undershaft's is to make weapons—and they make a deal to go see each other's workplaces. Despite the fact that they have quite different conceptions of morality and right/wrong, Barbara and her father seem open to learning about the "other side." We'll see how that goes . . .
Climax (Crisis, Turning Point)
Major Disappointment
When Act 2 picks up at the Salvation Army, we get a quick glimpse of Barbara in her element, enthusiastically feeding the hungry/poor, recruiting, and converting (or at least attempting to convert) visitors to the Army. However, Barbara's idealism and enthusiasm take a big hit when Mrs. Baines, the Army commissioner, opts to take a huge donation from a whisky kingpin and—yes, you probably guessed it already—Barbara's father. Barbara had been maintaining that the Army couldn't be bought—the only thing it was interested in was helping others achieve salvation—but Mrs. Baines gleefully accepts the money, as they desperately needed it. Baines is elated, but Barbara is devastated.
Falling Action
Field Trip to the Gun Cotton Shack
When we pick up the next day, Barbara is at home, having quit the Salvation Army, and she definitely seems bummed out. Various members of the family start trickling in. Lady Brit gets Andrew to promise that he will keep providing adequate salaries for the girls for the indefinite future. Then, Andrew, Lady Brit, and Stephen discuss Stephen's career prospects. The discussion gets a bit heated; it seems that Stephen remains the one lone wolf among Andrew's children who isn't charmed by him. Once all the children and their fiancés have arrived at Lady Brit's house, they go as a group to see Andrew Undershaft's factory
Resolution (Denouement)
All's Well That Ends With Gunpowder
Once they all see the factory, everyone is mighty impressed, albeit for different reasons. Lady Brit suggests that if Andrew won't leave the company to Stephen, he might consider Adolphus. Undershaft initially dismisses the suggestion, since Dolly isn't a foundling, but then Dolly reveals he is, actually, since his parents' marriage wasn't legal in England. So, Dolly and Undershaft haggle about salary, and then Dolly agrees to take on the job. Much to Dolly's surprise, Barbara is supportive; she thinks that the factory and its workers will be a very fertile recruiting ground for her efforts for the Salvation Army, which she plans to rejoin.