There are a bunch of plot lines in The Return of the King: Aragorn's adventures on the Paths of the Dead, Gandalf and Pippin's stay in Gondor, Éowyn's disguised battle with the Nazgûl and her romance with Faramir, and the list goes on. But behind all of them is the Ring Quest, which is the whole reason this series exists. So we are going to focus on the Ring plot in our analyses here.
At the beginning of Book Six, we return to Frodo and Sam. Where last we left off at the end of The Two Towers, Frodo had been poisoned by the giant spider Shelob and taken prisoner by orcs. Sam managed to grab the Ring from Frodo before he was taken away (so the Ring is still safe from Sauron). But poor Frodo is now trapped in the tower of Cirith Ungol while the newest Ring-bearer, Sam, struggles to get him out.
Sam faces two choices: either leave Frodo in the hands of the orcs and complete the Ring Quest himself or return for Frodo and forget about the Ring Quest for the time being. Sam loves Frodo so much—and is so humble about his own abilities—that he decides to turn back and rescue Frodo rather than seizing the glory (and misery) of the Ring Quest for himself. It's Sam's good nature that keeps him from falling for the evil spell of the Ring, and it's a good thing, too.
The conflict in The Return of the King is pretty obvious: Frodo and Sam have to sneak quietly into the heart of enemy territory, carrying the one thing that Sauron wants most in the world. This is not an ideal situation (understatement of the decade). From the moment that Sam rescues Frodo from the orcs at Cirith Ungol, to the part when the slave driver pushing a band of orcs through Mordor mistakes Frodo and Sam for a couple of stray miniature orcs, to the section when Gollum attacks Frodo and Sam physically as they trudge up the side of Mount Doom, these two get no peace from the evils of Mordor.
Frodo and Sam's battles with the cruel territory and evil inhabitants of Mordor are bad enough. What makes the conflict of this part of the Ring quest even worse is that Frodo must also constantly fight against himself and his growing urge to take the ring for himself and wreak all kinds of havoc. When Sam rescues Frodo from Cirith Ungol in Chapter One, Frodo briefly turns on Sam for daring to take the Ring from him. And as Frodo trudges along through Mordor, his internal struggle with the Ring makes him weaker and weaker, because his inner difficulties are taking their physical toll. Even though he is in the middle of a war zone, for Pete's sake, Frodo finally just takes off all of his armor and drops his weapons because he is too tired to carry them. Through the Ring's horrible influence, Frodo is becoming his own worst enemy.
At last, still pretty early on in Book Six, we see our heroes reach their destination, Mount Doom. Frodo rushes ahead into the Sammath Naur, the Cracks of Doom, while Sam fights off traitorous Gollum. But now that they have reached this awful, belching volcano…
… they have to actually chuck the ring in, which is proving easier said than done. The great suspense, not only of Chapter Three of The Return of the King, but also of the whole Lord of the Rings series is, will Frodo actually be able to destroy the Ring when it comes down to it? After all, the Ring's power corrupts and damages minds, and Sammath Naur is at the heart of the Ring's Master's kingdom—surely the place where its influence is strongest. What is more, Frodo has been showing signs of possession by the Ring for ages, long before we even reach The Return of the King Book Six (see Frodo's "Character Analysis" for more on this). So the suspense is pretty intense.
Frodo does not have the strength to destroy the Ring, but it's fine, because Gollum bites his finger off and falls into the Cracks of Doom with the Ring. Problem solved. We can all go home.
Okay, okay. To be fair, Gollum does not intentionally save Frodo or the world. He wants to take the Ring for himself. Driven mad, Gollum jumps on Frodo at the edge of the Cracks of Doom and gnaws his finger off. But Gollum soon loses his balance and, with the Ring and Frodo's poor finger still in his hands, he falls into the fires of Mount Doom.
The great trick of Tolkien's conclusion to the Ring quest plot is that what we thought mattered most throughout the whole series—Frodo's power of resistance against the Ring—turns out not to be his saving grace. Finally, standing in the crater of Mount Doom, Frodo claims the Ring for his own. (Really, dude? Now? After holding out for hundreds of miles of travel?) But Frodo's failure to resist the Ring ultimately proves only that he is mortal. Everyone makes mistakes, and Frodo turns out to be no exception.
What matters is that Frodo is merciful. By sparing Gollum's life against the advice of both Sam and Faramir, Frodo leaves himself a loophole. As an ordinary being, Frodo is doomed to fail in his quest to resist this superhuman temptation. But his mercy leaves room for the most unexpected of forces (Gollum) to intervene to save him (and the world) in spite of his mistakes. For more on the morality of this conclusion, check out "What's Up With the Ending?" and our "Character Analyses" of Frodo and Gollum.
By Book Six, Chapter Nine, the wrongs of Middle-earth have been mostly righted. Aragorn has been crowned High King of Gondor and has finally married Arwen Evenstar; Rohan has Éomer as its new lord; the Shire has been cleared of Saruman's horrible half-goblin people; and Sam has married and started a family with his beloved Rosie. We're done here, folks.
Of course, we have to mention that all of these nice things have been made possible by Frodo's horrible trip to Mordor. Unfortunately, not everything is coming up roses for our favorite hobbit. Having seen what he has seen, Frodo feels that he has outgrown the Shire. So when the elves decide that it is time for them to leave Middle-earth to men like Aragorn, Frodo agrees to go with them to the West. Once Frodo leaves Middle-earth, the Ring Quest has truly concluded, and the last remnant of Sauron's power has departed the world. Now we're done.