This question originally appeared on Quora. 
Answer by Trevor Sullivan, Student of Linguistics and Tolkien fan
I have studied both Sindarin and Quenya, and I can say they are extremely difficult to learn, for three main reasons:
1: They are based on non-germanic languages. I am an English speaker, and I assume you are too. English is a Germanic Language, and for those who speak English, Germanic languages are easier to pick up (German, Dutch, OE, Swiss German, etc). However, Sindarin is based on Celtic languages like Welsh and Irish, which have some rules and constructions that are nonsensical to Germanic speakers, such as affection and lenition (Changing all the vowels in a word to change number, and changing the first letter of a word to reflect case, respectively). Quenya is based on Romance grammar (Latin, in particular) with Finno-Ugric phonology. It is polysyntactic (which means that a single word can regularly have tons of affixes loaded onto it) and has over ten noun cases.
2: They are useless. It's sad to say, but there are very VERY few people who know these languages well, mainly because of #3.
3: They are incomplete. The languages have fairly small vocabularies, not quite large enough to be able to function as a speakable language. The grammar rules are complete, but Tolkien never decided on the words for several concepts, and others he has ignored completely. He was more interested in the grammar behind the language, and the script it is written in than the vocabulary of the language, which is unfortunate. The language may become speakable when the full lexicon is released (and Christopher Tolkien is determined not to release it, so this probably won't happen until the copyright expires in 2063 or Congress gets their act together and shortens the copyright term. The entire life of the author plus 90 years is ludicrous. I don't think the Professor cares about how much profit his works are making, considering he died in 1973).
I learned from two books, "Pedin Edhellen" and "Quetin i Lambe Eldavia," both of which are available on this website:
Navaer, melyn!