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Whether you learned a second language by drills, flashcards, and rote repetition, or by visiting a foreign country for the summer, there is likely a language theory that matches your method. Familiarity with the bases of such approaches will help you formulate your teaching strategy for adults. From the time of ancient Greece to well into the last century, new languages were almost invariably taught by what is often called the "audio-lingual method." If your high school French class involved a lot of rote learning, repetition, oral and written testing, emphases on grammar and translation, and constant correction by your teacher, you're already familiar with this method. In the last half-century or so, a more (so-called) "natural approach" has become predominant. It tries to replicate the childhood process of acquiring a language through immersion, play and tasks, constant usage in a low-pressure environment, and indirect emphases on grammar and vocabulary. Modern "natural" or "immersion" methods encourage leaners to jump right in to the foreign language without the drudgery of vocabulary lists, grammar lessons, and constant repetition. Therefore, they are often a more appealing prospect to harried, hurried adult learners. Such task-based methods are based on the premise that students will naturally "work out" vocabulary and grammar as they interact with the language (and the other students). The struggle to do so, essentially, is part of the learning process. Critics, however, say that this leaves too much vital material for the student to address on his or her own, and that the teacher's guiding hand in areas like grammar is vital, even if it can sometimes be less than enthralling. Despite the reputation they've assumed as "boring," "sterile," and "outdated," there is a reason why classic approaches were used almost exclusively for thousands of years. Even in the modern world, they can still have a place in the language classroom. The "audio-lingual" emphasis on habit formation, mimicry, memorization, and repetition can provide a clearer sense of the goals, processes, and achievements for some students. Likewise, a focus on grammar and translation, guided in the first language, can build essential skills that some adult learners may be keen to acquire. That said, for many adults, traditional methods will feel too much like being back in school as children, and can dissuade them from continuing the process with enthusiasm. This is why variety and flexibility in your teaching methods are essential. For all the value in understanding theories, learning happens in practice and usually, through practice. Simply put, teaching an adult a foreign language requires not only your mastery of the language as a teacher, but also a clear understanding of your student's background, motivation, goals, learning style, and needs. Holding fast to traditional methods simply because they have been in use for centuries is usually not the answer, nor is tossing all the old ways aside for the new vogue in language education. It is up to you, the teacher, to determine the mix that will work best for your classroom and your student(s).
Compare classic and modern approaches. See the pros and possible cons of newer views. Don't ignore traditional methods. Find the right balance.