Linguistics is the scientific study of language. Someone who engages in this study is called a linguist. More specific fields include xenolinguistics, which focuses on alien languages, and archaeolinguistics, which is the study of ancient or dead languages.
Richard Boswell graduated from Starfleet Academy with a major in linguistics and served as a linguist on the USS Benjamin Franklin from 2357 to 2361. He later taught at Starfleet Academy for four years. (Star Trek: Remington)
Timothy Sinclair had a natural talent for linguistics, which was honed during his childhood training at Enclave J-12. He developed an intuitive, almost instinctual, ability to learn and understand most unfamiliar languages he encountered. From 2376 to 2378, he held a position as an archaeolinguist with the Daystrom Institute. Sinclair returned to that position briefly after his second retirement from Starfleet in 2385. (Star Trek: Pendragon)
Benjamin Caldwell was altered by an alien artifact sometime prior to 2360, giving him an unnatural ability with languages. Naturally, he entered linguistics in Starfleet and has held the position of chief linguistics officer aboard the USS Galaxy and USS Cantabrian. (Star Trek: The Cantabrian Expeditions: "Catalyst, Part One", "Breaking Benjamin", "Better the Devil You Know")