During an outdoor movie event, Marge remembers of going to Barnacle Bay, an island she visited in childhood. Homer takes her there, but when the family arrives they discover it has become positively poor.
The Simpson family goes to see an outdoor movie in the park, but when they get there, the entire area is crammed with people, except for one spot. They race The Van Houten Family to the space, and Homer succeeds by wrapping a picnic blanket around Maggie and throwing her into the space, where she uses the blanket and parachutes down to fill the space. When the silent black and white film Ned Flanders brings fails to please the audience, Patty and Selma produce one of their many old-fashioned film reels and play a movie of Marge's childhood paradise, an island called Barnacle Bay.
Homer takes the family to the island, where they discover that it is a disgusting slum full of loungers and drug addicts. On the night they stay, Homer gets a group of out-of-business entrepreneurs to rebuild the carousel Marge used to ride on, and invites Marge to ride on it with him. While Bart and Lisa power the carousel from underneath it, Homer sets off a fireworks display, attracting a huge crowd, then accidentally sets the dock on fire, burning it and the carousel completely down. The residents of the island (that are bullies of Homer) bully him by picking on him, beating him up, taking his clothes and shoes off him, tieing his wrists and hands to each other, and hanging him to a winch, putting a fish hook in his nose and tieing him to the winch until Marge comes and releases him. They find out that the island's economy failed when overfishing drove away the prized Yum-Yum Fish, and Homer promises to bring the fish back to the island to repay the damages.
While Homer is on a boat fishing, Marge and Lisa visit a storm watching center and find out that a massive storm is heading right for where Homer is. On the ship, Homer mixes up his directions and "puts bait on the steak and beer-batters the fish hooks", but the batter brings back the Yum-Yum Fish. Homer briefly finds joy in fatally clubbing the hundreds of fish they catch when the storm strikes. When the compartment for the life raft is opened, there is no raft, just Bart.
The ship has to stay afloat on large waves, and finally, the fishermen encounter a huge wave they barely are able to climb over. Behind it, there is a mountainous wave ten times higher than the first one but their ship gets destroyed by the wave. Ned bullies Homer by beating up Homer and connecting Homer to a fish winch, putting a hook in Homer's nose and hanging to the winch. When the storm blows over, they are rescued by the Japanese fishing ship Iruka-koroshi-maru (いるかころし丸 Dolphin Killer), but are thought dead by the islanders. As a memorial service occurs back on the island, Homer, Bart and the ship's crew burst in and everyone goes out to catch Yum-Yum Fish with Homer's new recipe. However, Lisa bars the way and warns the islanders that overfishing the fish will only bring the island its former woes again. Of course for a fishing island to give up its fish it has to do something just as profitable instead, and much to Lisa's objection, the villagers abandon the fishing trade and begin giant scale logging operations all over the island.