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
Rollin' on the River
Marlow is sailing down the Thames in the Nellie when he decides to tell a story. A long story. Act I of his story begins when he gets a job in Brussels and then heads down the Outer and Central Stations in Africa. Turns out, life in Africa isn't so great. The black Africans work under appallingly inhumane conditions and it's all pretty gross. The one cool thing is that he hears about this guy, Kurtz. Kurtz sounds pretty neat, and Marlow is stoked to meet him—but he's delayed by a series of, well, delays.
You're right; this sounds like a whole lot of nothing. The point is, the first act ends when Marlow finally heads up the Congo with a crew of unlikable "pilgrims" and a Company manager and his uncle.
Act II
Mr. Kurtz, I Presume
Marlow learns more about Kurtz by eavesdropping on the manager and his uncle, like that they want to be promoted and that Kurtz's stunning outputs of ivory threaten their ambition. Meanwhile, the whole journey is kind of nightmarish—there are cannibals, and then they get attacked by a group of Africans. The one high point is when Marlow finds a seaman's book in an abandoned hut.
At the Inner Station, Marlow meets a weird guy who we call the harlequin. He knows Kurtz, so Marlow cozies up to him to get more info. It seems that Kurtz has allied himself with the native Africans and uses them to raid other villages and steal ivory. Meanwhile, the Africans worship him as a god. All this suits Kurtz so well that he orders the African's to attack Marlow's steamboat; he doesn't want to be taken away from the interior and his precious ivory stash.
At this point, we see Kurtz for the first time. It's not very inspiring, seeing as he's sick and apparently incapable of walking. But he is capable of crawling, so he tries to make a run for it by crawling out of the tent. Marlow—being still able to walk on two feet—easily overtakes him and carts him off down the Congo. Where he dies. Horribly.
At this point, with Kurtz dead and Marlow half-dead himself, we're going to call an end to Act II.
Act III
Return to Normalcy
Marlow finds himself ostracized by his crew and unable to return to a normal life. So he concerns himself instead with returning Kurtz's letters to his fiancée—who still thinks he's the bee's knees. She's so wrong that she actually thinks that the last words Kurtz said were her name. And Marlow actually lets her believe that, meaning that he's … learned a lesson? Changed? Matured? Lost his illusions?
You tell us.