Tolkien developed an interest in languages at an early age. By the time he was a young adult he had already created many languages. It was in the early 1930’s that Tolkien started creating a language for the Elves of the Third Clan. Sindarin was created in 1944. It was heavily inspired by his fictional language Noldorin (based on the Welsh language) mixed with another one of his languages.
Many languages Tolkien created were inspired by Old English, Old Norse, Welsh and even Finnish.
Quenya (another Elvish language) was mostly reserved for poetry, magic, song and lament. Sindarin was the spoken language. Quenya is mostly based on the Finnish language, in Middle Earth cannon Sindarin is a descendant of Quenya. Which is why there are some Finnish sounds. The reason why Welsh is also so present in the languages is because it is one of Tolkien’s favourite languages, he enjoyed the sound of it (which explains the similarities in sound between Sindarin and Welsh).

While people can learn the languages, there are many websites with dictionaries and alphabets, but it is very hard to have normal conversations in it. These languages were created for a magical fictional word, so asking your friend to come over and watch your favourite tv show with you is going to be pretty hard.
Sindarin grammar is based on Welsh grammar (just like the sound), it has many Celtic influences and Germanic ones as well. In fact, Tolkien was a scholar of both Old English and Old Norse which can be traced in a lot of his works. 

https://www.omniglot.com/conscripts/sindarin.htm