Arwen in the books
Arwen appears in two chapters of ‘The Return of the King’: on the last page of 6.05. The Steward and the King she arrives in Minas Tirith to marry Aragorn; and in 6.06. Many Partings she talks to Frodo and gives him her place on the ship to Valinor. After that, she is mentioned a couple of times, once when Gimli and Éomer debate the beauty of Galadriel, once when the party travels to Edoras for King Théoden’s funeral; and once when she stays behind in Edoras to part with her brothers, as her husband accompanies the Hobbits home.
She is mentioned earlier on in the book, twice, when the standard she made for Aragorn is mentioned.
The main body of her story is told in Appendix A(v), The Tale of Arwen and Aragorn.

Arwen in the movie
As always, Arwen’s part was expanded for the movie, to incorporate the story of Arwen and Aragorn in the larger body of the War of the Ring. When we first see her, she is travelling to the Grey Havens, to take the ship into the West. But she is halted by a vision of her son, Eldarion, which she sees as a sign that there is still hope. She returns to Rivendell to confront her father, who admits that he had seen the child in their future; but he doesn’t believe that Aragorn will be able to turn the tide, and claim the throne of Gondor as well as defeat Sauron.
Arwen’s faith however, is not only renewed by reinforced, and she asks Elrond to reforge Narsil. In one shot, she is reading a book about the Paths of the Dead, so presumably she is the one who gives Elrond the idea of letting Aragorn assemble the Army of the Dead.

At the same time though, Arwen seems to be becoming ill. On the audio commentary track for ‘The Return of the King’, Boyens and Walsh explain this as a result of Arwen giving up her immortality: because she is one of the last born of her kind, she is also more vulnerable to Sauron’s evil. As it spreads, with the War at the point of breaking out, Arwen becomes weakened by exposure to Sauron’s darkness. The Evenstar darkening seems a symbol of that.
In Dunharrow, Aragorn has a dream about Arwen dying. A little later, Elrond arrives at the camp to hand him Andúril, and confirms the vision in his dream. This adds an extra drive to Aragorn’s quest for the White City: he has his lover to save now, too. He also understand that despite his letting go of her, Arwen made her choice to stay in Middle-earth.
During the extended scene with the palantír, Aragorn once again sees Arwen, fading and dying; which causes him to drop the Evenstar.

Arwen re-appears at the coronation however, in a pretty lime-green dress carrying a standard of the White Tree, the emblem of Gondor. She is reunited with Aragorn, which results in laughter, giggles and one huge, passionate kiss. Their wedding is not shown.

Changes from book to movie
Most of the aforementioned material was made up by the script writers; which is odd because most actual Arwen-stuff was left out:
– In the books, Halbarad gives Aragorn the standard Arwen made for him, a sign of hope yet also a signal that it is time for Aragorn to claim the throne of Gondor. The standard is unfurled for the first time when the Black Ships come into Minas Tirith.
In the movie, the banner is replaced with Andúril, brought to Aragorn by Elrond, but makes a cameo-appearance at the coronation, where it is not black but white.
– Arwen arrives way after the coronation, and after Aragorn finds a scion of Nimloth, causing the whole Fellowship to remain in Minas Tirith because Aragorn doesn’t want them to leave: ‘I would have you wait a little while longer: for the end of the deeds that you have shared in has not yet come. A day draws near that I have looked for in all the years of my manhood, and when it comes I would have my friends beside me. [6.V.]
The wedding itself, though obviously a big thing for Aragorn, is dealt with in one sentence: And Aragorn the King Elessar wedded Arwen Undómiel in the City of the Kings upon the day of Midsummer, and the tale of their long waiting and labours was come to fulfilment. [6.V.]
– Tolkien then describes Arwen singing a song about Valinor to Aragorn, sitting in the Court of the Fountain, when Frodo comes to Aragorn and asks leave to depart from Minas Tirith and visit Bilbo in Rivendell. Arwen speaks comforting words to Frodo, and gives him her necklace for comfort, and her place on the ship to Valinor.
In the movie, Frodo just boards the ship. The necklace was the inspiration for the Evenstar, the device that symbolises Arwen’s immortality and commitment to Aragorn.
– Arwen then travels with the rest of Aragorn’s household, and the remains of the Fellowship, to Edoras for Théoden’s funeral. She remains there to say goodbye to her brothers. Since Théoden wasn’t buried in the movie, and Arwen doesn’t have brothers either, both passages were left out.