As told in "The Tale of Aragorn and Arwen" Aragorn in his twentieth year met Arwen for the first time in Rivendell, where he lived under Elrond's protection. Arwen, then over 2,700 years old, had recently returned to her father's home after living for a while with her grandmother Lady Galadriel in Lórien.
Aragorn fell in love with Arwen at first sight. Some thirty years later, the two were reunited in Lórien. Arwen reciprocated Aragorn's love, and on the mound of Cerin Amroth they committed themselves to marry one another.
While Aragorn was out in the War, Arwen made, with her hands, the Livery of Elendil in mithril, gems and gold on black cloth. This was taken by her brothers and a group of Rangers of the North to Aragorn before taking the Paths of the Dead, and was an encouraging sign for him to take the difficult path. It was unfurled at the Battle of the Pelennor Fields to triumphantly announce the King's return.