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)
There's this unnamed guy who's only been captain of a ship for two weeks. He's sailing along the coast of Siam (or present-day Thailand) and feeling lonely because his crew is really tight-knit and he's an outsider. On top of all that, he feels like they're constantly questioning his judgment. He often finds himself doing the same, too.
One evening while performing the night watch, the captain glances over the side of his boat and hey what do you know, there's a naked dude in the water. The guy introduces himself as Leggatt and says he's on the run after murdering a guy on his ship, which is anchored nearby. The lonely captain feels like this guy can be his bestie, so he pulls him on board and hides him in his private captain's room.
Rising Action (Conflict, Complication)
There are a bunch of close calls as nosey and meddling crewmates buzz around the captain's room. As you can probably imagine, it's not very easy to hide a person on an old wooden ship for long. Eventually, the skipper of Leggatt's ship comes looking for him with a goon squad, but the captain-narrator manages to hide Leggatt well enough to convince them that the fugitive must have drowned in the ocean. Still, Leggatt realizes after this incident that he can't stay on the ship much longer. As much as it pains the captain-narrator, Leggatt will have to jump off the boat in the middle of the night and swim for one of the nearby islands to have any hope of starting a new life.
Climax (Crisis, Turning Point)
The captain-narrator agrees to steer his ship as close to the nearby islands as possible so Leggatt will have a good chance of reaching the shore. He also gives Leggatt some money and a hat so the South Pacific sun won't burn his head and face. Back on deck, he orders his crew to steer the boat toward the nearby islands in the middle of the night. This move is extremely dangerous, since the men can't see the land and might crash on the rocks at any second. The only thing that saves them in the end is the captain's hat, which the captain spies floating in the ocean. He uses the hat's position to help guide the boat back to safety.
Falling Action
Once the boat has successfully pulled away from the island and its dangerous rocks, the captain runs to the back of his ship and looks for Leggatt in the water. But he can't see anything except his hat floating in the ocean. He is hopeful that Leggatt was able to swim to safety and that the dude will have a good life.
Resolution (Denouement)
In his final thoughts, the captain-narrator even envies Leggatt for being off the ship and being free. It's clear that the captain feels trapped by loneliness and by the opinions of his crewmembers. His last words suggest that some part of him has left the ship with Leggatt, the part of him that feels free and valuable as a person.