The Great Journey
After the defeat of Melkor, the Valar debated the fate of the Elves - whether they should be left to dwell in Middle-earth, or brought to Valinor to be kept under the direct protection of the Valar. It was decided to bring them to the land of the Valar, and Oromë was sent back to Cuiviénen to summon them.
When he returned, though, he found that the Elves feared the Valar, and were reluctant to make the journey. Three ambassadors were chosen, Ingwë, Finwë and Elwë, to travel to Aman with Oromë, and help the Elves decide on their course. These three were filled with awe by what they saw there, and by the light of the Two Trees, and counselled their people to follow the summons.
The followers of Ingwë, and most of the peoples of Finwë and Elwë agreed, and set out on the Great Journey westwards across the wide lands of Middle-earth. These were the peoples later known as the Three Kindreds, the Vanyar, the Noldor and the Teleri. Not all the Elves obeyed the summons; those who refused are known as Avari, the Unwilling2.
Oromë led the peoples of the Three Kindreds out of the east of Middle-earth. The Vanyar were the least numerous, and the most eager to reach Aman, and they came first on the Journey, followed by the Noldor of Finwë.
The Teleri, led by Elwë and his brother Olwë, were the greatest host, and many were uncertain and doubtful. Not a few of these people left the Journey and remained in Middle-earth3. The most notable of those who turned from the Journey were the Nandor, who were led away down the Vales of Anduin by Lenwë.
At last, the Vanyar and the Noldor reached the shores of the Great Sea, in the regions between the Bay of Balar and the Firth of Drengist (regions later known, at least for the most part, as the Falas). Ulmo brought a great island to the shores, and on it transported the Elves to Aman.
The Teleri were the hindcomers, though, and arrived in Beleriand too late to embark on Ulmo's island. They dwelt for a while on the banks of the Gelion in eastern Beleriand, but later spread to the shores. In this time, two events of historical importance occurred - their lord Elwë was lost for a time in Nan Elmoth, and they encountered Ossë, a Maia of the Sea.
Many of the Teleri wished to remain in Beleriand, some to seek for their lost lord, and others because of desires stirred in their hearts by Ossë. When the time came for Ulmo to return to Beleriand to take the Teleri to Valinor, then, many of them remained behind. These people became known in after years as the Sindar, the Grey-elves, and those who dwelt by the shores under the lordship of Círdan became known as the Falathrim.
Melkor Chained: Three Ages of Bliss
Now came three ages of glory and bliss for the Elves, both east and west of the Great Sea. In Valinor, the Vanyar and the Noldor, and those of the Teleri who completed the Journey, dwelt with the Valar and learned from them. They dwelt in the jewelled city of Tirion in the Pass of Light, and at the Swanhaven of Alqualondë, and beneath the tower of Avallónë on the Lonely Isle of Tol Eressëa. While the Two Trees still gave light to the realm of the Valar, three ages passed, and the Elves of Valinor became the wisest and noblest of all the Children of Ilúvatar.
Meanwhile, in Beleriand, the Sindar dwelt beneath starlight. While most of Middle-earth still slept, awaiting the coming of the Sun and Moon, Melian the Maia brought life to the forests and plains of Beleriand under Thingol's rule, and Oromë would still ride at times across the darkling lands.
The Nature of the Elves
Both Elves and Men are the Children of Ilúvatar, and so have much in common, but there are also great differences between the two peoples. Of these, the most significant is that Elves are 'immortal', at least while the World lasts; they do not suffer ageing1 or disease, and if they are slain or wither with grief, they are reincarnated in the Halls of Mandos in Valinor.
Although, unlike Men, the Elves must remain in the world until its ending, they are not bound to Middle-earth. They may if they wish take the straight road, and sail into the Uttermost West, a road that is barred to mortals.
Elves also have far clearer sight and perception than Men; they are naturally aware of many things that are hidden from the Younger Children, but these gifts are not without limit.
The Elves never had any distinct 'religion' in the sense that Men would understand the word; indeed, the High Elves had travelled to Valinor and lived with the Valar (or 'gods') themselves for many ages before Men came into the world.
Of all the Valar, they most revered Varda Elentári, the spouse of Manwë; and Lady of the Stars. In Middle-earth, they called her Elbereth, Star-Queen, and sang to her across the wide ocean Belegaer. Great respect was also given to Ulmo, especially during the First Age when he aided the Elves against Morgoth.