As the play opens, a woman named Lady Britomart is trying to arrange the family finances with the "help" of her son, Stephen. We put "help" in "quotes" because the super bossy and commanding Lady Britomart doesn't actually need any assistance in coming up with opinions, but for some reason she's making a big show of getting Stephen to weigh in. The topic of the day? How to make sure her daughters (Stephen's sisters) have enough money to live once they're married to their fiancés, who aren't likely to be the best providers (at least in the near future).
Lady Britomart bullies Stephen into "advising" her to get some help from his father, Andrew Undershaft. The only catch? He and Lady Brit have been separated for a looooooong time. It seems that Lady Brit kicked her husband to the curb when she realized he was going to disinherit Stephen from the family business as part of an Undershaft family tradition of only passing the business on to a foundling—an abandoned child taken in and adopted by the family. However, Andrew has been financially supporting the family since then, and Lady Brit (er, Stephen, that is) seems to think that getting some extra moolah from him is the only way to keep her girls going in their marriages.
So, in an effort to grease the wheels for that request, she's invited Andrew to the house to see the children for the first time in years and meet the girls' fiancés. It's super awkward when he arrives, since he doesn't initially know which of the people there are actually his offspring. Luckily for him, he figures it out soon enough and they all have a decently pleasant conversation.
One point of tension, though, is the fact that his daughter Barbara is a "Major" for the Salvation Army, so she's not the biggest fan of the fact that her dad makes weapons for a living and therefore profits off violence and death. However, after some banter on the topic, they strike a deal: Undershaft will visit her Army headquarters, and she will visit his factory.
In the second act, we see how Undershaft's visit to Barbara goes. We get a glimpse into the lives of some of the people who go to the Army for help and food, including Snobby Price and Rummy Mitchens. Both Price and Mitchens have claimed to be more downtrodden and poorly behaved than they actually are to solicit the interest of the Army's workers. Also, there's a mean dude named Bill floating around trying to find his girlfriend, and he ends up hitting one of the Army workers, Jenny Hill, because he thinks she was involved in convincing his girlfriend to leave him (and he also hits Rummy because she's in his way... like we said, he's quite the charmer).
Barbara tries to convert Bill, but she is unsuccessful. He ends up trying to buy his salvation with a sovereign (a gold coin), but Barbara won't accept it and Snobby Price proceeds to steal the sovereign.
A bit later, Mrs. Baines—an Army commissioner—arrives and is super excited to report that they've received a huge donation that will likely clear up their money woes. However, there's a catch: The person donating it is a whiskey distiller, and he's requiring that the Army find some other people willing to donate an equal amount. Undershaft offers to put up the rest of the money, and Barbara is horrified to realize the Salvation Army will be saved by a whiskey distiller and an arms manufacturer, both of whose businesses go against the Army mission.
However, Mrs. Baines is unconcerned about the moral dilemma this presents, and the rest of the people present (including Barbara's fiancé, Adolphus a.k.a. "Dolly," who has been bonding with Undershaft) go marching off in a procession to get more converts with this good news in hand. Barbara is devastated that the Army was so easily bought…
Act 3 opens at Lady Brit's house, where Sarah and Barbara are hanging out. It appears that Barbara has quit the Salvation Army. Dolly shows up hung over from the previous night's celebrations, and then Undershaft arrives to take everyone to his factory. While the young ones are off getting ready to leave, Lady Brit gets him to promise to take financial care of the girls going forward. Success. Also, Undershaft, Stephen, and Lady Brit discuss Stephen's future, if he's not to inherit the family business.
Then they all head off to the factory, where everyone is really impressed—even Barbara. They end up figuring out that Dolly can be Undershaft's "foundling," since his parents' marriage isn't legal in England, and so he ends up agreeing to take over the family business. Barbara is fine with this, since she's decided to return to the Army and set her mind to converting the workers at the factory, who will (she has decided) be more ready to accept religion "for real" (as opposed to just for food/shelter). And so, er, there's your happy ending.