How did it happen in the movie?
The next morning, Celeborn and Galadriel send the Fellowship off on their journey. Celeborn tells Aragorn that the shores are being watched, and gives him a nice little dagger. Galadriel speaks ominous words of parting, and refers to Arwen’s promise.
Every Fellowship member receives a gift (except for ol’ Boro, who only gets the same cloak everyone else got), and the company are provided with said cloaks, lembas (Elvish waybread) and of course boats. Frodo receives a small phail, containing some light of Eärendil.

How did it happen in the book?
The same evening Frodo and Sam survive the not-so-nice encounter with their future selves in Galadriel’s Mirror, the Fellowship prepares to depart. They are summoned to Celeborn‘s chamber, where the decision is made that no one stays behind, and they will travel further by boat. During the debate afterwards, Boromir makes it clear he still wants to travel to Minas Tirith, as was his original intention. It is clear by now that Aragorn means to go on with Frodo.

In the morning, as the Fellowship is packing, they receive a gift of lembas, Elvish way-bread, which Gimli mistakes for cram, a way-bread made by the men of Dale. They also receive cloaks, made by the Lady herself, with a small leaf-brooch. The cloaks are extremely light, and change colour. When, after a long journey, they arrive at their boats, Sam discovers ropes made of hithlain, yet another gift. All of these will prove to come in handy as the company will go further on their way.

When they have departed they are greeted by the Swan boat of Celeborn and Galadriel. Galadriel sings a lament for them, and they are invited to dinner on a small island in the stream. There, each companion receives a gift:
– Aragorn gets a nicely embroidered sheath for Andúril, and he also receives the Elfstone, which will later cause the people of Gondor to name him Elessar.
– Boromir gets a belt of gold. Frodo recalls this belt as he is talking to Faramir, which helps him win the Gondorian’s trust.
– Merry and Pippin get small silver belts.
– Legolas gets a nice new bow, with which he will attempt to shoot a fell beast from the sky on the banks of the Anduin.
– Sam gets a small box with seeds, which he will plant after the scouring of the Shire.
– Gimli, who can pick his own gift, asks for a single strand of hair from Galadriel‘s head. He gets three of them. He has the most useless gift of all, really.
– Frodo gets the star-glass, the phial of Galadriel, which contains some light of the star of Ëarendil. This of course will prove very useful indeed, when confronted with huge hairy spiders.

At their parting, Galadriel sings yet another song, this time in Elvish, and with Gimli complaining to Legolas about his broken heart, this chapter ends.

Not only did Boromir get absolutely nothing, Aragorn didn’t get the Elfstone, Merry and Pippin got daggers instead of beautiful silver belts and Sam got some rope. Which in the books, everybody got. Also, there was no Merry and Pippin eating too much lembas.

Mistakes
– Galadriel pronounces ‘Eärendil’ incorrectly: it should be ay-ar-en-deel rather than ar-en-deel.

Borrowed Lines
– Celeborn stole his line about the cloaks, ‘Never before have we clad strangers in the garb of our own people. May these cloaks help shield you from unfriendly eyes’, from an anonymous Elf, who says: ‘You will find them a great aid in keeping out of the sight of unfriendly eyes… (…) Never before have we clad strangers in the garb of our people’ [2.VIII.FtL]

– Another anonymous Elf, who informs Gimli that ‘We call it lembas or waybread…’ provided Legolas with his gleeful shout: ‘Lembas! Elvish waybread.’ [2.VIII.FtL]

– Not only did Boromir not get his golden belt, he also didn’t get to say ‘The Orcs prowl on the east-shore; if you go forward, peril will grow with every mile…’ In stead, it is Celeborn who warns Aragorn for the danger: ‘With every league you travel south the danger will increase. Mordor Orcs now hold the eastern shore of the Anduin.’ [2.IX.GR]

– Legolas has the same problem, his ‘Seldom will Orcs journey in the open under the sun, yet these have done so’ is also borrowed by Celeborn. [3.IV.RoR]

– Galadriel gives Sam a rope, saying: ‘And for you, Samwise Gamgee, Elven rope made of hithlain.’ This line was borrowed from yet another anonymous Elf (let’s call him Figwit), who says about the ropes in the boats: ‘They are made of hithlain.’ [2.VIII.FtL]

– Gimli, in asking his gift from the Lady Galadriel, which is ‘to look upon the Lady of the Galadhrim one last time, for she is more fair than all the jewels beneath the earth’, borrows his own words from his first meeting with the lady where he says ‘…the Lady Galadriel is above all the jewels that lie beneath the earth!’ [2.VII.MoG]

– Like mother, like son-in-law: Galadriel’s ‘Am meleth dîn. I ant e guil Arwen Undómiel pelitha’ (which means: For her love, I fear the grace of Arwen Evenstar will diminish) is a line Elrond speaks to Aragorn in Appendix A (v): ‘Arwen Undómiel shall not diminish her life’s grace for less cause.’ She does the same thing when borrowing Elrond’s ‘A great doom awaits you, either to rise above the height of all your fathers since the days of Elendil, or to fall into darkness with all that is left of your kin’ from the same Appendix A(v), and turning it into: ‘You have your own choice to make, Aragorn: to rise above the height of all your fathers since the days of Elendil – or to fall into darkness with all that is left of your kin.’

Bookie Details
– Galadriel’s swan-boat was a nice touch, though it hardly made up for the lack of singing.
– It was nice to see some lines from Appendix A (v), The Tale of Aragorn and Arwen, re-appear into the movie.