From the original article by Luke Smith.
From Gottfriend Hensel's 1791 Synopsis Universae Philologiae
I've said on a couple livestreams that the ideal way for an English speaker to begin learning or excel in learning other major European languages (Spanish, French, Italian and German) is to use Michel Thomas's audiotapes. They can be found for free on Pirate Bay and other sites, but you can also buy them on his official site.
This style of audiotapes is so far above any other, it's hard to even put it in words. They make really exceptional promises: "learn a language in 8 hours" and in some sense I'm inclined to agree.
They certainly give a reflexive foundation that makes learning anything else about a language very easy. There are multiple courses and they're worth listening to multiple times until it's a totally internalized.
The tapes all have Thomas locked in a room with two people who don't know the language, one male, one female. Thomas simply teaches and illicit basic responses from the two students, teaching them as they go. As the listener, your part is to say the proper responses to yourself before the example students. At all points in time, the students are creating novel sentences, combining basic concepts.
Probably the most important part of the tapes is the lack of vocabulary taught. You don't get 20 irrelevant nouns with each lesson to memorize that you don't even now how to use. What new words you "learn" are mostly shared in common with English. The goal is to make you fluent before you have to memorize words.
Thomas, instead, actually teaches the language and how to be constructive in it: the verbs, the verb inflections, how to combine them, basic pronouns and the like. Only once the students understand them does he move on to the words for real-world objects. Thomas will sometimes explain why he does this in the course, but it amounts to what I've said in other places: you can guess or figure out nouns or talk around them, but if you don't know how to put verbs together, you just don't know the language and you can't even fake it. It is much easier to learn nouns after you actually learn the structure of the language and can actually use them.
You're never told to "listen to this passage and think about what it means" in the Thomas method. The Thomas method is entirely productive: you make the sentences and you have to put yourself in the mindset of how the language works.
A lot of other audiotapes, say Pimsleur, have you sit and listen to text and implicitly ask you to "translate" it. This in essense, keeps you thinking in English, or thinking in translating mode. The also keep you chained to canned responses in a single dialog. When people do this, they ignore the actual structure/grammar of the language, listen for big noticable nouns, and then piece together what the sentence means. This is always a bad idea.
It's honestly rare that you even ever see a "good teacher." By that I mean someone who can easily keep track of what his students know and can devise questions perfect to pry their knowledge. Thomas is just honestly good at this and it goes a long way. In the tapes, if he notices that a student repeatedly messing something up, he knows how to elicit better responses and remind them of what they need. This is 99% of teaching, despite the fact that it's a really rare skill.
After Michel Thomas's death (or perhaps a little before) the company running his website above put out tapes for many other languages: Chinese, Arabic, Hindi, Japanese, etc. under his name. They are done "in his method" theoretically, but they are no good. They do weird things like have two different teachers: one who instructs the students and one who is a native speaker of the language to say the sentences in it. I think the idea behind it was to make sure you hear a "perfect" accent, but it's a total waste and the sponteneity required for actual teaching is lost because you have these two different people trying organize among themselves. I think the teachers lack the introspective skill to keep tabs on the students' learning that I mentioned above, so all-in-all, I think they're awkward and fake.
Donovan Nagel (you may know him from his YouTube channel on BSD) gave Michel Thomas a negative review after using the "Michel Thomas" Arabic tapes. I listened to part of the Chinese tapes and they were not worth it (if you want to learn Chinese I've written about what I recommend).
But the real Michel Thomas tapes: Spanish, French, Italian, German, done by the man himself, are the best for all their respective languages.