The Teleri were the greatest host of the Eldar. They had two kings, the brothers Elwë Singollo (or Elu Thingol as he was later known in the Sindarin tongue) and Olwë. When the Teleri reached Beleriand during the Great March from Cuivienen, Thingol went wandering in the forests as was his wont. In the forest of Nan Elmoth he met Melian, one of the Maiar. They fell in love, and with Melian, Thingol stood spellbound in Nan Elmoth for several years.
In the meantime, Olwë and many of the Teleri could not delay longer, and went to Aman without him Elwë and his following. Elwë's followers stayed in Beleriand, to search for their king. At long last he awoke from the spell and set up a kingdom in the midst of Beleriand: Eglador (Land of the Forsaken, or Land of the Elves. The etymology is not clear.). The Dwarves of Nogrod and Belegost in the Ered Luin (Blue Mountains) were contracted to aid in the building of the city of Menegroth (the Thousand Caves).
Other Teleri also stayed behind: these were the friends of Ossë the Maia, who had fallen in love with the shores of Middle-earth, and did not wish to depart. Their leader was Círdan, and they established cities at Eglarest and Brithombar. They were known as the Falathrim, or Elves of the Falas (Shore). They were not part of the realm of Eglador, but still took Thingol as their High King.
Yet other stray bands of Teleri settled in Nevrast and Hithlum to the north of Eglador, although these did not form any realms.
The Teleri of Eglador, the northlands, and the Falas were collectively known as the Sindar, or Grey Elves, in later days, because they developed a civilisation all its own, which almost equalled that of the Calaquendi or Light Elves of Valinor.
A last group of Teleri in Beleriand were the Laiquendi or Green Elves: they were descended from the Nandor, which had split from the Great March before the Hithaeglir (Misty Mountains), and gone south along the Great River (Anduin). A part of them, under Denethor son of Dan, crossed the Blue Mountains eventually, and settled in Ossiriand, or as it was later known Lindon (land of the singers). They remained a people apart for long, although many of them removed to Thingol's realm after Denethor was killed.
Just before the arrival of the Noldorin exiles, the dark lord Morgoth returned to his old stronghold of Angband, and his activities increased. Thingol had Melian use her magic to create a girdle of bewilderment around Eglador, so that nobody could enter without the king's permission. Ever after it was known as Doriath (Land of the Fence). Thingol remained nominally high king of Beleriand, although especially the Noldor following of the sons of Fëanor usually ignored his commands.
The language of the Sindar diverged from common Telerin over the long ages they were sundered from their kin, and became known as Sindarin. By the time the Noldor arrived in Beleriand, the languages had become mutually unintelligible, but the Noldor were quick to learn it. In the Second and Third Age, Sindarin became known as the Noble Tongue, and became the Elvish tongue used in daily speech throughout Middle-earth. It was also adopted for daily use by the Númenóreans, and remained somewhat in use in the Realms in Exile of Gondor and Arnor.
Sindarin even replaced Noldorin Quenya as the language used by the Noldor in Beleriand, even in predominantly Noldorin settlements such as Gondolin, although Quenya survived as a language of knowledge.
The Peredhil, Elrond and Elros, were partially of Sindarin Elven descent, as their mother Elwing was the daughter of Dior, the son of Lúthien, the daughter of Thingol and Melian.
For more information, see The Silmarillion.
An excellent resource for Sindarin can be found at: http://groups.msn.com/laurelindorean