How did it happen in the movie?
Lord Of the Rings: Fellowship Of the Ring opens with a thrilling prologue that tells the story of the movie’s main character: the One Ring. Galadriel, the Lady of Lothlórien, takes us on a journey through time to the second age and the forging of the Great Rings of Power.
We are introduced to the three leading races of Middle Earth: the Elves, the Dwarves and the Men – and to Sauron, who forged the Rings of Power so he could control them all by means of his own, secret Ring.
A Ring he loses when in the Battle of the Last Alliance, fought on the slopes of Mount Doom, Isildur Elendil’s son avenges his father’s death by cutting the finger wearing it off Sauron’s hand. Ignoring Elf lord Elrond’s advice, Isildur keeps the Ring as a future heirloom but it betrays him to his death and ends up forgotten in a muddy riverbed.
But the Ring is found by the creature Gollum, who takes it with him to the Misty Mountains where it prolongs his life unnaturally until it is taken from him – by accident – by the Hobbit Bilbo Baggins.

How did it happen in the book?
Place in the book
Tolkien opens Lord Of the Rings: The Fellowship Of the Ring with a prologue, but nothing quite like this: Concerning Hobbits is a small introduction to the Hobbits and their lifestyle, giving the reader just enough background to be able to begin to read, but nothing more. The EE scene that bears the same name is only a very small sample of what this introduction to the trilogy is like.
The information that the movie audience receives in the Prologue is actually taken from two separate chapters: 1.II The Shadow Of the Past, where Gandalf tells Frodo all about the Ring and 2.II The Council Of Elrond, where lord Elrond himself gives an almost complete account of the history of the Ring.

The Forging of the Rings
Because they had to present a lot of information in a relatively short sequence, you get a rather odd idea about the creation of the Ring: it is presented as if Sauron, looking like a miniature version of Barad-dûr, gives the Rings of Power to the leaders of the free peoples and then deceives them by forging his very own, even more powerful version.
However, Sauron at the time went under a fair disguise and thus befriended the Elf smiths of Eregion, whom he taught the art of forging Rings of Power. When he returned to Mount Doom he forged his own Ruling Ring, and putting it on he pronounced the Ring-spell. This was overheard by Celebrimbor, leader of the Elf smiths, who instantly knew they had been betrayed.
The Elves then took their Rings off, and hid the three most powerful ones: Vilya, the Ring of Air, given to Gil-Galad (who passes it on to Elrond), Nenya, the Ring of Water, kept by Galadriel and Narya, the Ring of Fire, which is passed from Círdan onto Mithrandir.

The Battle of the Last Alliance
Because of the pacing and the limited time, an event that takes up eight years is comprised in one single moment: the so-called battle of the Last Alliance is actually the battle of Dagorlad in the year 3434 of the second age. This event, where Sauron’s forces are defeated, is followed by the siege of Barad-dûr, which ends seven years later with Elendil and Gil-Galad wrestling Sauron but perishing in the act, and Isildur cutting off the Ruling Ring with the broken sword Narsil. Who in fact overthrows Sauron is not completely clear, though Isildur claims (as is stated in ‘The Silmarillion’) that he took the Ring as compensation for the loss of his father ánd because he was the one who’s slain Sauron – thus laying aside the advice of Elrond Peredhil and Círdan.

The Legend of the Ring
Gollum, who was actually a sort of Hobbit called Sméagol, is not the first one to find the Ring (the movie implies that he is): his cousin Déagol found it, but Sméagol desired to have it so very much that he killed him for it.
Bilbo Baggins does not simply pick up the Ring and run away with it. As is told in ‘The Hobbit’ (the prequel to LOTR), Bilbo finds the Ring and then has to play a riddle game with Gollum to find the exit of the caves he’s in. Because Gollum can’t solve the final riddle (What do I have in my pocket?), Bilbo wins but Gollum breaks the bet and returns to his little island, where he discovers his precious (as he calls the Ring) is lost. Only then does he start shouting: ‘Lost, lost, our precious is lost!’ – which you can clearly hear him wail in the background of this scene.

Mistakes
– In the beginning of the sequence, you see three Elf Lords receiving three Rings of Power. These are supposed to be Círdan, Gil-Galad and Galadriel – but Tolkien describes Círdan as having a beard!
– When Isildur takes the Ring you can clearly see that he is wearing gloves. However, in the scroll Gandalf reads in Minas Tirith, Isildur speaks of how his hand was scorched by the Ring, and how he thinks he would never rid of the pain. So either the Ring should have burned through the fabric, or Isildur did not wear gloves when he picked it up.

Borrowed Lines
– The lines with which Galadriel opens the Prologue, she borrowed from Treebeard in 6.VI [Many Partings]: Treebeard says goodbye to the Lord and Lady of Lothlórien by saying: ‘It is sad that we should meet only thus at the ending. For the world is changing: I feel it in the water, I feel it in the earth, and I smell it in the air. I do not think we will meet again.’
Galadriel’s ‘I amar prestar aen, han mathon ne nen, han mathon ne chae, a han noston ned gwilith’ is a rough translation of this: ‘The world is changed. I feel it in the water, I feel it in the earth, I smell it in the air.’

Bookie Details
– The Orcs of Sauron are described by Aragorn as bearing a Red Eye as symbol [3.I.]. This is very well depicted here.
– Gil-Galad is shown for a few seconds in the Prologue, and you can actually see him stab an Orc with his spear Aeglos, which is mentioned at the Council scene as a pendant to Elendil’s sword Narsil.
– The account of how Isildur lost the Ring is actually quite accurate: Isildur, thinking that all his enemies are slain, neglects to post enough guards outside his camp near Loeg Ningloron (the Gladden Fields). When the camp is attacked by Orcs, Isildur manages to escape using the Ring to make him invisible, but the Orcs follow his trail of smell and when Isildur tries to escape by jumping into the Anduin, the Ring avenges his original master by slipping off his finger.
– On the extended edition of FOTR, Galadriel shows her Ring, Nenya, to Frodo. It is also called the Ring of Adamant, and it looks very similar to Tolkien’s description of it: a ‘ring wrought of mithril, that bore a single white stone flickering like a frosty star’. [6.IX]