Dictionaries define a linguist as a person who is accomplished in languages, especially someone who speaks several languages. By this definition, Tolkien was a consummate linguist, having learned more than a dozen languages and teaching one of them — Anglo-Saxon. In addition, Tolkien invented several languages, many of which are featured in his tales of Middle-earth.
Keep in mind that none of the languages that Tolkien invented for his Middle-earth mythologies is fully formed. You can learn the vocabulary and syntax rules for some of his more complete languages, such as Quenya, the so-called High Elvish. But you can't actually speak or write anything you want in any of these languages because, even where Tolkien fully developed the grammar, he didn't have the opportunity or need to develop a full vocabulary as well.
The etymological mythmaker
Etymology refers to studying the history of a word by tracing its development from its earliest known sources, analyzing its components, and tracking down its cognates to a common ancestral source. In many ways, Tolkien was a consummate "etymological" mythmaker. He often seems to have developed his stories as explanations of the history of particular terms.
You can't help but wonder if all of Tolkien's myths recounted in the Quenta Silmarillion (History of the Silmarils) of The Silmarillion stem from his fascination with the sound of the name Éarendel in Cynewulf's poem Crist:
Hail Éarendel, the brightest of angels sent to the world of men
Éarendel was an Old English term for a ray of light that seems also to have signified the morning star (Venus) with its Christian symbolism related to John the Baptist and Christ. Tolkien may have seen the potential in this name for developing a pre-Christian myth that later would be fulfilled in the gospels.
In the Quenta Silmarillion, though, the reader learns that Eärendil (Tolkien's spelling of Éarendel) was the brightest angel (messenger) because he wore the sole-surviving Silmaril on his brow — a jewel that carried the last vestige of the blended light of the Two Trees of the Blessed Realm. Eärendil was sent by the Valar of the Blessed Realm and sailed over Middle-earth in his ship Vingilot ("Foam-Flower") as a symbol of promise and hope to all people that they may yet prevail against evil, even as the Valar prevailed over Morgoth by ejecting him into the void.
One can easily see how the story explaining the significance of Eärendil and his appearance over Middle-earth could spawn stories about how the Silmarils came into being and how the Elves and Morgoth contended over them in a long war in Middle-earth — as well as later stories of how Men rose and fell in Númenor and battled the reemerging evil of Morgoth's lieutenant Sauron.
Whether the myth of Eärendil was the real genesis of the many other sagas recounted in The Silmarillion, The Hobbit, and The Lord of the Rings is not nearly as important as understanding how the history of a word can indeed generate myth. Tolkien was a great storyteller because he demonstrated over and over the process by which people create their treasured myths — a process that can begin with the origin and history of one name or term.
Invented language and its need for a mythology
Tolkien clearly believed that fabricating a language was a futile business if you weren't also willing to create a history or mythology for it to express. This was the basis of Tolkien's criticism of Esperanto, the language invented to facilitate communication between all the peoples of the world and that few people learn and fewer bother to use. In Tolkien's estimation, constructed languages such as Esperanto are doomed from the get-go because they have no history or legends, just syntax, grammar, and a way of building vocabulary. Pretty boring stuff for most of us. By contrast, Tolkien's rich mythologies provide not only contexts for characters to express feelings and thoughts, but also histories explaining how their languages evolved.
One important example of language history in Tolkien's tales is the story of the prohibition on the older form of Elvish called Quenya, spoken by the Elves in Aman, and how this ban in Middle-earth affected the acceptance and development of a younger dialect called Sindarin.
According to The Silmarillion, the Elvish language split in part because of a political decision — a prohibition of the older language. The King of Doriath, learning of the slaying of his Telerin kin in Aman by the Noldorin rebels under Fëanor, forbade the use of their language, Quenya, within his kingdom in Middle-earth. Underscoring this split with the older form of Elvish (supposedly spoken by the Valar as well in Valinor), the King of Doriath even changed his name from its Quenyan form, Elwë Singollo, to its Sindarin form, Elu Thingol.
Because of the ban, Quenya ceased to develop in Middle-earth. Unlike Sindarin, it became a "dead" language, reserved for writing only. Given this political climate, it's always interesting to note when Tolkien has one of his Noldorin Elf characters break Thingol's ban and use Quenya.
One example of defiance of this ban occurs in The Silmarillion when Aredhel, the White Lady of the Noldor who was forcibly wedded to the Sindarin Elf Eöl, named their child Lómion (Quenyan for "Child of Twilight"). The child's father, however, gave him the Sindarin name Maeglin ("Sharp Glance"), the name the boy took and used when he betrayed the Noldorin Kingdom of Gondolin.
Another example of flouting the ban occurs in The Lord of the Rings when Galadriel bids farewell to the Fellowship by singing a song, now generally known as Namárië (Quenyan for "Farewell"), which Frodo recognizes as being in the "language of Elven song" (Quenya) and speaking of things seldom heard of in Middle-earth (the song laments the loss of Valinor).
Galadriel's quoting of Namárië is one of the few instances of more than a simple phrase or two of Quenya in The Lord of the Rings, where the Elves primarily use Sindarin. By inserting the Namárië in an otherwise Sindarin environment, Tolkien not only subtly introduces the bad blood between the Noldorin and Teleri Elves and all woes in Aman and Middle-earth, but also gives us a sweet taste of what's been lost because of the ban. Tolkien concretely demonstrates how compelling a constructed language can be as the centerpiece of a convincing history and legend.