1. At the beginning of the Second Age, Elrond dwelt in the Household of the High King Gil-galad, in Lindon.
As noted in Gil-galad's Biography, Elrond and Gil-galad are distant cousins, through their respective ancestors Turgon and Fingolfin.
2. Sauron, using the name Annatar [Lord of Gifts], tried to corrupt the Elves: aware of their love for all things beautiful, he suggested that, by joining powers, they could make a new Valinor out of Middle-earth. Elrond, Gil-galad and Círdan understood his true desire and rejected his offers.
3. Using Sauron's knowledge, the forging of the Rings of Power began in Eregion. Of the 20 rings that were made, only the Three - Vilya [the Ring of Air], Narya [the Ring of Fire] and Nenya [the Ring of Adamant] - were free from Sauron's influence. Celebrimbor, the smith, gave Narya and Vilya to Gil-galad's safekeeping, and Nenya to Galadriel.
"Three Rings for the Elven-Kings under the sky." [LotR]
Please note that there are two differing version of the Tale - one account states that Gil-galad passed Narya on to Círdan during the siege of Mordor. However, it was also written that this exchange took place soon after Celebrimbor had given the Ring to Gil-galad.
3. The war between Sauron and the Elves began.
4. [II 1695] Sauron marched on Eriador. Gil-galad sent out an army, commanded by Elrond, who was later joined by Celeborn and his Elves. However, Sauron's forces were stronger, and held both armies off, as he took Eregion [II 1697].
5. Sauron directed his attention to defeating Elrond's small host of Elves who had escaped from Eregion. The Elves were outnumbered and came close to falling, but Sauron was weakened by an attack by Dwarves of Khazad-Dûm and Elves.
"Bearing as a banner Celebrimbor's body hung upon a pole, shot through with Orc-arrows, he turned upon the forces of Elrond." [UT]
"He would indeed have been overwhelmed had not Sauron host been attacked in the rear; for Durin sent out a force of Dwarves from Khazad-dûm, and with them came Elves of Lórinand led by Amroth." [UT]
6. Elrond fled to the north, and came upon a hidden valley in the Misty Mountains, where he founded the haven of Imladris or Rivendell [Deep Dale of the Cleft], also called by some "The Last Homely House". [II 1697]
"The stronghold and refuge of Imladris, that Men called Rivendell, was founded by Elrond Half-elven; and long it endured." [S]
For further on Imladris, please visit its page.
7. Sauron, in his quest for the Three, turned to Lindon, where Gil-galad reigned. Imladris still stood, though besieged. The need to divide his army to stop Elrond advancing would be Sauron's downfall. Eriador was freed.
"His force was weakened by the necessity of leaving a strong detachment to contain Elrond." [UT]
"The army that was besieging Imladris was caught between Elrond and Gil-galad, and utterly destroyed. Eriador was cleared of the enemy, but lay largely in ruins." [UT]
8. Celeborn dwelt in Imladris for some time. Galadriel, feeling the need to be closer to the sea, crossed Mória and joined him there. With her she took their daughter, Celebrían... and Elrond fell in love.
"It was then that Elrond first saw Celebrían, and loved her, though he said nothing of it." [UT]
9. The first White Council took place, attended by the Wise of Middle-earth. During this Council, Gil-galad made Elrond Vice-regent of Eriador, and gave him Vilya, the Ring of Air, the Ring of Sapphire, "the mightiest of the Three" [RotK]. Imladris replaced Eregion as the Elvish stronghold in Eastern Eriador.
Note that, in the Third Age, this Council would be echoed and its title re-used. There are, thus, three Councils in which Elrond takes place: the "White Council" of the Second Age, the "White Council" of the Third Age and the aptly-named "Council of Elrond".
For further on Vilya, please visit its page.
10. Celebrían left Imladris when Galadriel and Celeborn moved to the land between the Mouth of the Gwathló and Ethir Anduin. Elrond had not yet asked her to betroth herself to him.
11. In an effort to defeat the Dark Lord Sauron, Elendil and Gil-galad, old allies, joined their forces and their armies, in what would become known as "The Last Alliance of Men and Elves". Elrond marched with the Elvish army, as herald to Gil-galad.
"I remember well the splendour of their banners." [Elrond, FotR]
"Never again shall there be any such league of Elves and Men; for Men multiply and the Firstborn decrease, and the two kindreds are estranged." [Elrond, FotR]
12. The Alliance left Imladris and made for Dagorlad, the Plains facing the fortresses of Mordor, where they were met by Sauron's forces.
"All living things were divided in that day, and some of every kind, even of beasts and birds, were found in either host, save the Elves only. They alone were undivided and followed Gil-galad. Of the Dwarves few fought upon either side; but the kindred of Durin of Moria fought against Sauron." [S]
13. Elrond fought with the Last Alliance at the Battle of Dagorlad. And - though many Elves and many Men perished - this battle was won, through the might of the High King Gil-galad and his spear Aeglos, and of King Elendil and his sword Narsil.
"We had the mastery: for the Spear of Gil-galad and the Sword of Elendil, Aeglos and Narsil, none could withstand." [Elrond, FotR]
14. Having achieved victory in the Battle of Dagorlad, the Last Alliance gained entrance to Mordor and spent 7 years at the siege of Gorgoroth. On the slopes of Mount Doom [Orodruin], Sauron was defeated, but Gil-galad perished at his hand. So did Elendil, and his sword Narsil was broken beneath him as he fell.
"[Isildur] alone stood by his father in that last mortal contest; and by Gil-galad only Círdan stood, and I." [Elrond, FotR]
"And Gil-galad and Elendil were no more." [Elrond, FotR]
"The blade was broken and its light was extinguished, and it was not forged anew. And Master Elrond foretold that this would not be done until the Ruling Ring should be found again and Sauron should return." [S]
15. After Isildur, Elendil's Son, cut the One Ring from Sauron's finger with one of the shards of Narsil, Elrond and Círdan, on the slopes of Orodruin, advised him to cast it into the fires that raged inside, where it had been forged. But the Ring took control of Isildur and he kept it for himself.
"Isildur took it, as should not have been. It should have been cast then into Orodruin's fire nigh at hand where it was made." [Elrond, FotR]
"Isildur would not surrender it to Elrond and Círdan who stood by. They counselled him to cast it into the fire of Orodruin nigh at hand, in which it had been forged, so that it should perish, and the power of Sauron be for ever diminished, and he should remain only as a shadow of malice in the wilderness. But Isildur refused this counsel." [S]
"In the hour that Isildur took the Ring and would not surrender it, this doom was wrought, that Sauron should return." [Elrond, The Silmarillion]
It should be noted that, in the film version, only Elrond (and not Círdan) is present in Orodruin when Isildur keeps the Ring.
16. With the defeat of Sauron ended the Second Age. The Third Age began and, after Isildur's death, the One Ring remained hidden for many centuries...
"The Ruling Ring passed out of all knowledge, and the Three were released from its dominion." [Elrond, FotR]
"Sauron was diminished, but not destroyed. His Ring was lost but not unmade. The Dark Tower was broken, but its foundations were not removed; for they were made with the power of the Ring, and while it remains they will endure." [Elrond, FotR]