I can understand that many see Reginald Foster as an iconic latin teacher. Se also other background article
Especially due to his career as the Popes own latinist in the Vatican, as described in this article in The New Criterion.
He also appeared in this 2010 tv show as "The Latin King", where learning latin from Reginald Foster is compared to learning painting from Picasso or learning music from Mozart.
He is also know from appearing in Bill Mahers documentary about religion, called "Religulous" where he made some very bold quotes about the Vatican.
Here is a video of him teaching a class filled with many of his former students
Previously he also appeared regularly in the Vatican Radio show called "Latin Lover" where he made on the fly translations of various sentences.
Lately he published a book about latin named Ossa Latinitas Sola, The mere bones of Latin
But what is his concrete method for learning latin and how does it differ from traditional methods?