A Very Brief Summary
Bilbo Baggins, hero of The Hobbit, is feeling restless and irritable. At his own birthday party, he arranges an elaborate practical joke with the magic ring he picked up on his travels, which can make him invisible. In the middle of his scheme, Bilbo slips away, preparing to leave the Shire for good. He leaves his home and his Ring to his heir, Frodo Baggins, before taking off into the night.
After many years, Gandalf arrives in the Shire with urgent news for Frodo. This pretty golden Ring? It's actually the One Ring of the Dark Lord Sauron, which contains a portion of Sauron's power. The Ring will corrupt anyone who wears it. Look at Gollum, the owner of the Ring before Bilbo found it: he is now a twisted, desperate little creature. The Ring is inherently evil: all it wants is to make its way back to its Master, and so it will betray anyone who carries it. Gandalf tells Frodo he has to get out of the Shire ASAP because forces from Sauron will be coming to look for it.
Gandalf leaves the Shire, and Frodo waits and waits to hear from him. Finally, when Gandalf does not appear, Frodo sets out as planned with his trusty gardener Sam and his cousins, Merry and Pippin. Frodo & Co. plan to head to Rivendell, the dwelling place of the Elves in the North; but as they set out in the direction of the town of Bree, they hear rumors of some rather terrifying Black Riders who are asking with great interest after Mr. Frodo Baggins. Frodo wants to stay out of sight, so he leads his three companions into the Old Forest, as a shortcut to Bree. But Frodo's shortcut is a disaster: only with the help of a man named Tom Bombadil do they survive their run-ins with an evil willow tree and some scary Barrow-downs.
At Bree, the four Hobbits hang out at the inn, The Prancing Pony. After an accidental (and frankly, quite stupid) disappearing act by Frodo, they meet Strider (also known as Aragorn). He is a friend of Gandalf and says he'll help the Hobbits. Strider and the four Hobbits head to Rivendell, but the Black Riders track them down. Turns out that these Riders are Ringwraiths, nine great kings of men who have been corrupted by the power of Sauron. Frodo puts on the Ring in a moment of weakness and is stabbed by the leader of the Black Riders; his wound has the power to make Frodo into a wraith himself, so his companions must get him help (and quickly!). After a speedy trip to Rivendell, dodging Black Riders and relying on an Elf-lord, Glorfindel, for assistance, an unconscious Frodo and company make it to Rivendell.
When Frodo wakes up in Rivendell (thanks to Elrond, the lord of Rivendell, who has saved Frodo's life with his healing power) he is overjoyed to see that Gandalf and Bilbo are both there. Now that Frodo (and the Ring) have arrived in Rivendell, it is time for all of the wise people gathered there to have a Council to decide what to do with the thing. The people at the Council speak of many things: the history of the One Ring, its danger to all mortals, and the necessity of its destruction. To destroy the Ring, some unlucky person has to go to Mount Doom, in the land of Mordor, to throw it back into the lava that Sauron used to make the Ring in the first place. If the Ring is destroyed, Sauron's power in Middle-earth will be broken forever. Frodo finally volunteers. Sam, of course, insists on going with him.
Elrond sets up a Fellowship of nine to accompany the Ring in secrecy: Frodo (of course), Sam, Gandalf, Aragorn, Boromir (at least as far as the road to Minas Tirith, when he will go back to his home country), Legolas (an Elf), Gimli (a Dwarf), and Frodo's cousins, Merry and Pippin.
The Fellowship sets out from Rivendell, traveling across the treacherous passes of the mountain Caradhras and almost freezing to death. New plan: they will go through the ancient Dwarf diggings in the Mines of Moria. Things don't go so well there: they encounter the Balrog of Morgoth, an ancient evil from the Elder Days of Middle-earth. Gandalf sends the Balrog falling into a pit, but the Balrog catches Gandalf as it goes down. So the Fellowship has now lost its leader and adviser. Aragorn takes a leadership role, but he's not too confident about it.
After a stopover in Lothlórien, where Frodo sees the Eye of Sauron in a magic mirror, they head down the River Anduin. But now what? Boromir really, really wants to go to Gondor. (And actually, he's been acting weird lately, Frodo notices.) Frodo must go to Mordor. But where will the rest of the Fellowship go? As Frodo considers this alone, Boromir is suddenly overwhelmed by the temptation to take the Ring for himself, so that he can protect Gondor and defeat Sauron. Frodo runs away from him, and Boromir repents of his actions and tries to call Frodo back. But it's too late, now: Frodo knows that the Ring will possess and destroy each of his companions as they travel. He must go into Mordor alone with his burden if he is going to have any chance of success.
Frodo starts stealthily preparing to leave his friends behind. Meanwhile, the only one who figures out where Frodo is going is Sam; he plunges into the river after Frodo and insists that Frodo needs at least one companion to go to Mordor with him: Sam himself. Frodo agrees gladly. So Frodo and Sam cross the River Anduin and start looking for a path through the rocky lands of Emyn Muil to get to Mordor.