Lord Celeborn (Sindarin for "Silver-tree") is co-ruler of Lothlórien, together with his wife, Lady Galadriel. Together they have a daughter, Celebrían, mother of Arwen, Elladan, and Elrohir. Celeborn, like Galadriel, was Elven royalty of the First Age. By the mid- to late-Third Age (1981 TA), Celeborn and Galadriel took up the rule of Lothlórien after the loss of Amroth, who had been King of the Golden Wood. In the Second Age, Celeborn fought more than once with the Great Spider Shelob, though he was unable to do more than restrain her until very recently.
Celeborn stayed for a time at Caras Gelebren in the Second Age, where he remained, leading the Bright Company even after Galadriel departed. He commanded much of the defence of the citadel of the Gwaith-i-Mírdain. Oranoril was on of his captains.
Lord Celeborn is met in Caras Galadhon in the Golden Wood (Lothlórien)
Vol. 2, Book 7:
Celeborn (Allegiance Hall)
After the fall of Mordor and the Conquest of Gorgoroth's pushes into the Dark Lord's former realm, Celeborn can be found in his court in Caras Galadhon, here acting as an Allegiance Hall for those who have pledged to the Elves of Lothlórien.
Celeborn (Dol Dhannen)
After the fall of Sauron, Celeborn can be found with Galadriel and the host of Lórien deep in the trees of Mirkwood [13.2S, 45.9W], cleansing the Greenwood and beginning the destruction of Dol Guldur, after which they can be found on Dol Dhannen, the Hill of Ruin with King Thranduil of the Woodland Realm.
The Black Book of Mordor:
Celeborn (Vales of Anduin)
Celeborn is seen briefly in Legolas's recounting of the meeting of the Men and Elves that lived near Mirkwood.
Celeborn (Mordor Besieged)
Celeborn is met again during the war of the Great Alliance against Sauron that ended the second age at Echad-in-Edhil in Mordor Besieged. He fights under the banner of Amroth, King of Lórien since his father's death early in the siege of Mordor.
Celeborn travels south to Minas Tirith at Midsummer for his granddaughter's wedding. He can be found in the feast-hall of Merethrond after the wedding ceremony, seated at the high table beside Galadriel.
Celeborn (Morgul Vale)
Celeborn appears in the Morgul Vale, both just outside the entrance to Torech Ungol[61.4S, 4.5E] and within[33.8N, 13.4E], where he is organizing an assault on the Remmorchant, where Ungwetári hides.