The language of the Grey-elves (Sindar) of Beleriand was the most commonly used of the Elf-tongues in Middle-Earth. It was the most prominent descendant, with the Quenya, of the Common Eldarin, the languages speaking by the Elves who make the Great March.

When the Noldor returned to Middle-earth at the beginning of the First Age, the Noldor and the Sindar were not able to understand each other since their languages have developed differently during their long separation. The Noldor learnt Sindarin quickly and even started to render their Quenya names into Grey-elven.

King Thingol of Doriath forbidden the used of their tongue, Quenya, when he learnt that the Noldor had killed many Teleri and stolen their ships to get back to Middle-earth; so the language of his people, Sindarin, came to dominate. Quenya, though, was still used as a language of ceremony and poetry.

The Sindarin tongue shared common roots with Quenya, and the two languages had many similar words. Sindarin was said to be more changeful than the older tongue, however, and there were a number of regional 'dialects' of the tongue. The Sindarin spoken in Doriath was said to be the highest and most noble form of the language.

In the movies, both Quenya and Sindarin are spoken at various times. Though Sindarin is mainly used conversationally by most Elves.

~: The Silmarillion and the Unfinished Tale, will give you all the history behind the language. :~