"The Method" is the name originally given by the media in the 1950's to a new "style" and technique of acting that was practiced by a new generation of film actors, spearheaded by James Dean and Marlon Brando. The technique they were using, which made them more real, complex and vulnerable than actors ever before, was taught to them at the Actors Studio in New York by the prominent acting teacher of the time: Lee Strasberg. Strasberg expanded and refined "The Method" over his long career in the theatre, but at its core, it is a collection of exercises and procedures that train the actor's 'instrument' to be responsive and expressive, logically analyze a scene, and then behave truthfully as their character would, under the circumstances of the scene. While it includes many exercises that tackle these various aspects of the actor's work (such as the "Relaxation", "Private Moment", "Song & Dance" and "Animal" exercises), the core of "The Method" is the work with "Affective Memory". I.e. "Sense Memory" and "Emotional Memory" exercises, which enable the actor to create any reality that is required by the play or film, and truly experiences what their character experiences.
For centuries, actors used to indicate what their characters were feeling using external conventional gestures. This convention of acting drastically changed with the appearance of Konstantin Stanislavsky (1863 - 1938) - a Russian theatre director, actor and teacher who posited that in order for acting to be good, the actor needs to really experience what their character is experiencing, and not merely pretend to or indicate it with external gestures. Stanislavsky formed the famous Moscow Art Theatre, and devoted his entire life to finding a "system" which would enable actors to do that. In 1923 the Moscow Art Theatre came to tour the US, and a young amateur theatre lover by the name of Lee Strasberg (1901 - 1982) saw their performances in New York. He was completely taken aback by the performances he saw, and mostly by how real every member of the ensemble seemed to be, which was a sharp contrast to the conventional "acting" he used to see on Broadway. When two members of the Moscow Art Theatre stayed in the US after the tour, Strasberg enrolled in the theatre school they opened in New York. There, he was exposed to "The Stanislavsky System", and from then on he devoted his life to further developing these techniques and adjusting them for the American stage and screen.
In 1931 Strasberg formed the groundbreaking Group Theatre, which had many future 'giants' among its ranks, such as acting teachers Stella Adler and Sanford Meisner, playwright Clifford Odets, and directors Harold Clurman and Elia Kazan. But the bulk of his work with actors was done at the famed Actors Studio in New York, of which he was the artistic director from 1951 until his death in 1982. It was the Studio under Lee's leadership that produced the first "Method Actors": James Dean, Marlon Brando, Paul Newman and Marilyn Monroe, who used the techniques they learned there to create real and moving performances on the stage and screen. They became instant idols for the 'youth generation' of the 1950's, and "The Method" became a household name in America. Over the next decades, The Actors Studio under Strasberg has produced scores of film stars: Shelley Winters, Eva Marie Saint, Eli Wallach, Martin Landau, Ellen Burstyn, Jane Fonda, Sally Field, Al Pacino, Robert De Niro, Harvey Keitel, Jon Voight, Dustin Hoffman, Bruce Dern, Jack Nicholson, Dennis Hopper and Christopher Walken. These actors helped cement "The Method"'s status as the most prominent acting technique in America, and the very foundation of modern American Acting.