Or course a potential student may rightly want to learn about methodology, and while they're at it, figure out how we do things. Yet when I talk to them I sometimes feel like a used car salesman, trying to sell a slick shiny car (myself). In any case, it's probably better to keep our sales pitch short and sweet; yet at the same time be honest, especially when their idea of cutting edge methodology is unstructured conversation class; but I'll come back to this.
So here's my typical answer. I usually start off by saying I use the Communicative Approach. The student tries to communicate something, hopefully something they find interesting and important, and I help them say it better. This is far better than a methodology based on the repetition of oral grammar structures, which has surprisingly met with some success here in Spain, though I'd say mainly through effective marketing.
In any case, the potential student might then justifiably wonder how I help them say it better. The answer is primarily via intensive feedback. If it's a private class with a conversation emphasis (which many students seem to favor), then as we're speaking, I'm also writing down corrections and reformulations, which I like to call upgrading.
I'll give an example of a correction. I recently fell on my bike in La Pinilla Bike Park and had to get around on crutches for a few weeks. So my student saw me hobbling to class and asked, 'Do you want that I help you?' Of course I accepted his gracious offer, but once in class I corrected the sentence, and also mentioned that this isn't the first time he's made this type of error: it's typical for him. It actually takes some effort to correct this sort of fossilized error. He needs to make an effort, and my job is to (gently) remind him. But he's a good student, bright and motivated, and he'll get it before long.
The other type of feedback I give my students is reformulation or upgrading. They say something which is perhaps comprehensible yet not 'natural': you probably would never hear a native speaker say it that way. Actually this happens all the time as students struggle to find the words to express themselves. Often my students will say something and then look at me questioningly to see if I upgrade it or correct it: they want to know if they got it right. Some students are even quite demanding in this way, and I spend the class racking my brain for the best reformulation (and writing it down of course).
By the way, the main advantage of private classes is that they get this type of intense individualized feedback. Obviously groups tend to get more general feedback on common mistakes and upgrades, but that's also dead useful.
Here's an example. Recently a student was telling me about his work, and to be truthful, I was having trouble following him. He was saying his customers were mainly rich foreigners, and saying something about 'the business segment'. It finally dawned on me that he was talking about his target market, so I wrote, 'Our target market is well-off foreigners'. So I summarized a paragraph of groping for words in one sentence: a good upgrade.
Effective reformulation often means focusing more on vocabulary (lexis) than on grammar. Their main obstacle to effective communication tends to be lexical rather than grammatical. They just don't know enough language items, such as collocations and chunks of language, to express themselves as well as they need to (not to mention to understand native speech). For example, in the above, 'My target market is well-off foreigners', the problem was lexical, not grammatical.
That's why my reformulations are almost always whole chunks of language rather than isolated bits and pieces. Above, I didn't just write down 'target', or even the collocation 'target market', but the whole sentence, so students learn collocations along with typical co-text, and in context. I feel this makes it more likely the student will eventually use it correctly.
Likewise, I wrote the whole sentence, 'Do you want me to help you?', and didn't go into a grammatical slot-and-filler approach explanation like, 'want + indirect object + infinitive'. Actually, at some point it's useful to briefly point this out too, but definitely steer clear of long-winded grammar explanations.
So far you may be under the impression that my classes are very output (speaking) oriented, but as you have seen, students do get language input in the form of reformulations. Here I'm going back to my earlier comment about unstructured conversation classes. If a class is just conversation, perhaps with some correction, they'll consolidate what they already know, but won't progress to a higher level.
In fact, in our endeavor to give students what they want, after all, the customer is always right!, we sometimes fall into the trap of giving them straight conversation classes, albeit with some correction thrown it; great for consolidation, but they don't move forward. Having said that, it seems a great many students need consolidation, but the teacher must be wary lest a point be reached where students feel they are no longer progressing (and no longer in need of the teacher's services).
So language input is paramount: becoming proficient in English means learning thousands and thousands of language items (not just isolated words), so best not to waste time and start exposing the students to as much new language as possible. Students can obviously get this from our 'teacher talk', for example, from our own contribution to a discussion.
In fact, I often write this down as well: language that I've come up with when discussing a topic and which I think is useful. At the end of an hour-and-a-half private class, students sometimes go away with two pages of feedback and new language. Now they go away and study it. In fact, one of my students has bound all my sheets of feedback together and made a sort of book.
In any case, regarding the input-output debate, to ensure varied and lexically rich input (like listenings), I always follow a course book. This provides far more language input than I could come up with on my own, and it clearly structures the class and speeds up language acquisition. It's true that in private classes we sometimes set it aside for a while (or a long while), but it's always there and clearly enriches the class.
So how do I explain all this to my students? OK, I tell them my methodology is communicative, though it also comes along with a big dollop of the Lexical Approach, as is crystal clear by all my references to lexis and chunks of language. But all of this is probably Greek to them, so I often end up talking about the feedback I give, the books I use, and my belief that consolidation activities alone aren't enough to reach a higher level. I end up talking about what I do rather than the methodology behind it.