There are a small but not insignificant number of people in the world who are experts in JRR Tolkien's invented languages. Of those, a handful can even speak one of the more complete languages fairly fluently, though it's true that even his most developed languages are not as extensive, certainly in vocabulary (the grammar is fairly complete), as a "real" language, one actually spoken as a first language by people in the modern world. Wanting to lay a framework that others could extend, however, he left many root meanings and lots of prefixes and suffixes so that one can construct many words (and thus sentences) that Tolkien himself may never have written or uttered but which a student of his languages could nonetheless understand. After all, he was a first-rate philologist and knew Latin, Greek, Old German, Old Norse, Finnish, and many other languages from which other, more modern languages like English, French, German, and Spanish developed, and he knew them inside and out, and understood the nature of language much like a Stephen Pinker or Noam Chomsky does.
It's no surprise then that such students exist and that the most dedicated of them have taken it upon themselves to ensure that Professor Tolkien's languages do not die, or survive embalmed in a linguistic museum so to speak, but continue to grow, to be spoken, written and read, and to this end some have even broken out of their fairly insular little linguistic clubs and Tolkien societies and deigned to make this knowledge available to anyone who wants to learn. To this point I've not seen it done well at all, or in any way accessibly; it seems to my mind that one would have to have some higher education in linguistics just to be able to follow the conversations these sort of people have amongst themselves. But then I found this site:
Which, although still in a beta state (as one can see from the URL), purports to teach a "normal" person the Sindarin language, which is one of Tolkien's Elvish languages and is probably the most fully developed. It is the Elvish found most often in his books, when Elvish is spoken. There is another Elvish language, Quenya, which is not often heard, because it was (in Tolkien's created world) chiefly spoken by those elves who had gone West, across the sea to Tol Eressëa or further on to Valinor, a semi-divine land forever beyond the reach of Man, and therefore which does not enter into many tales. The two languages are somewhat similar but are different enough that, if one were to imagine being incarnated in a world where the two were spoken, the speakers of Sindarin and Quenya could probably understand fragments of what the others were saying but would have difficulty truly having any sort of fluid conversation. It would be a bit like the situation with the modern Scandinavian languages, which are obviously related, and derive from a relatively recent common Norse tongue, but which still can in no way be considered interoperable. I've been informed of this by some of my good friends who live in the various Scandinavian countries and report that amongst, say, modern Danish, Swedish, Norwegian, and Icelandic speakers, most understand the other languages to various degrees, some more, some quite a bit less. I'm not a language expert so I can't be any more specific, unfortunately. Nor can I comment on the non-Elvish invented languages, except to say that they were all left in a "less finished" condition, according to Christopher Tolkien and others.
At any rate, I don't think I'll be attempting to learn either Sindarin or Quenya any time soon, much less Dwarvish, Entish, Stoor, Númenórean (later spoken in Gondor), the native tongue of Rohan, or the black speech of Mordor. That some people do speak at least the sylvan languages, and that others are attempting to learn and pass them on at this very minute, however, for some reason delights and encourages me. Maybe in my old age I can find time in my day and room in my mind to fit them in. Until then I would like to improve my French, Spanish, German, Italian, Hungarian, Finnish, Russian, Ukrainian, Greek, Latin, Hebrew, and Egyptian: Ancient, Hieratic, Coptic, and Modern. And of course, my English as well.