Middle-earth is now ''free'' of the shadow and menace of Melkor; although you must remember that Sauron and many of Melkor's other monsters and creatures remain in the North, albeit in hiding and in fear of the Valar. The scars of that terrible Battle of the Powers remain; mountains have been thrown down, valleys raised, seas have broken in upon the lands, and many lands have been broken; great black clouds have risen and obscure the sight of Varda's stars in the North. It was at this point that the Valar hold a council in Valinor and debate what ought to be done in the best interests of the Elves; whether they ought to abandon Middle-earth, which has no Sun, no Moon, and is therefore in perpetual twilight, or to come to the Blessed Realm and live in bliss at the feet of the Powers and under Eru. The Valar were divided over this point; for some, and of those Ulmo was the most outspoken, held that the Elves should be free, and left alone in Middle-earth, and with their arts to heal the hurts of Melkor. But others, fearing for the Elves in the gloaming and wild lands of Middle-earth, wanted them to remove to Valinor indefinately. Finally, a consensus was made, and the Elves were ordered to come to Valinor; and at this point Mandos, who until that moment had remained silent, said: ''So it is doomed.''
Oromë, therefore, returned to Middle-earth and sought for the Elves. (Rather interesting point here, that is not addressed by Tolkien, is what on earth happened to the guard about Cuiviénen!)But the Elves were filled with dread at these summons, having seen the Valar only in their wrath as they went to war. And so, Oromë chose three ambassadors from among the three kindreds of the Quendi who would go to Valinor and see for themselves; and these were Ingwë, Lord of the Vanyar, Finwë, Lord of the Noldor, and Elwë, Lord of the Teleri. On coming to the Blessed Realm, they were all filled with awe at the glory and majesty of the Valar, of their many mansions and gardens, and most of all at the beauty and radiance of the Two Trees of Valinor. And on returning to Middle-earth, they urged their peoples to hearken to the summons and abandon Middle-earth, which was for the most part dark and barren. And so began the Great Journey of the Eldar (that name was first given to the Quendi by the Vala Oromë, but has since only been used to refer to those of the Elves who embarked on the Great Journey), and the first great sundering of the Elves.
All of the Vanyar, under their lord Ingwë, went to Valinor. Most of the Noldor listened to Finwë and also embarked on that journey, but only a portion of the Teleri (but still a great host, greater than the others) passed into the West, under two lords Elwë and Olwë, most of them preferring the quiet and twilight of Middle-earth. The great host followed the Vala Oromë on his great horse Nahar. Many of the Elves on that Journey grew weary and many turned aside, out of fear of the ruins of War, or desiring to abide permanently besides many fair rivers and forests (these were all Telerin Elves). Eventually, they passed through a great forest (later called Greenwood the Great, and during Sauron's sojourn there, Mirkwood) and came to a great River (it was in fact Anduin, that River that was afterwards the great frontier of the West) and beyond that they caught sight of great mountains - the Hithaeglir, Towers of Mist, which were reared by Melkor to hinder the riding of Oromë, and many grew afraid and turned back, and were lost. The Vanyarin and Noldorin hosts passed over the River and were led by Oromë into the passes of the mountains, but the Teleri remained beside the banks of Anduin. And a certain Lenwë then led a great host of the Teleri (the people of Olwë) south down the vales of Anduin and was heard of not until many ages had passed (these Elves became known as the Nandor).
At last, the hosts of the Vanyar and Noldor scaled the Blue Mountains and came into the fair country of Beleriand; and at this point Oromë left them and departed over Sea to seek the counsel of Manwë. And a great many of the Teleri, under the lordship of Elwë, also crossed over the Misty Mountains, passed over the wide lands of Eriador and eventually came to the Blue Mountains, for Elwë wanted eagerly to return to Valinor, and he also had the friendship of Finwë, lord of the Noldor. At last, they too crossed the Blue Mountains and entered Beleriand; and set their camp by the River Gelion.
Sorry if this all seems dull or completely incomprehensible, but there is really no other way of telling it without missing out a great many important details. It would be nice, though, if someone read it! The above map is of Beleriand, the region on the north-western coast of Middle-earth in ancient days. The River Gelion is the long river that stretches from the lower regions of Ossiriand up to the March of Maedhros in the north (although at the time that the Telerin Elves made their camp at Gelion, Maedhros was not even born yet!) I hope the map makes it easier.