Brecht, from Germany was a playwright/producer/director of his own and other people’s plays. He also wrote a large amount about dramatic theory. When explaining his theory you need to do it in terms of his practice in writing and production.
The theory, arising from a Marxist notion of drama as a vehicle for rational didacticism describes theatre as Brecht, in a sense, what he wished it to become.
Brecht's view is that actor should not impersonate, but narrate actions of another person, as if quoting facial gesture and movement. Brecht uses the example of an accident-eyewitness. To show bystanders what happened, he may imitate, say, the victim's gait but will only quote what is relevant and necessary to his explanation. Moreover, the actor remains free to comment on what he shows.
As the audience is not to be allowed to identify with character, so, too, the actor is not to identify with him or her. Brecht agrees with Stanislavsky that, if the actor believes he is Lear, the audience will also believe it, and share his emotions. But, unlike Stanislavsky, he does not wish this to happen.
Alienation - http://beautifultrouble.org/theory/alienation-effect/
Brecht saw that these audiences were manipulated by theater technology — beautiful, realistic sets, cleverly naturalistic lighting, the imaginary fourth wall, and most importantly, emotionally effusive acting techniques. He soon watched with horror as the Nazi movement gained popular support in his country with its racist, xenophobic demagoguery, relying on similar emotional manipulation. Emotional manipulation was, to him, Enemy Number One of human decency. The alienation effect attempts to combat emotional manipulation in the theater, replacing it with an entertaining or surprising jolt. For instance, rather than investing in or “becoming” their characters, they might emotionally step away and demonstrate them with cool, witty, and skillful self-critique. The director could “break the fourth wall” and expose the technology of the theater to the audience in amusing ways. Or a technique known as the social gest could be used to expose unjust social power relationships so the audience sees these relationships in a new way. The social gest is an exaggerated gesture or action that is not to be taken literally but which critically demonstrates a social relationship or power imbalance. For example, workers in a corporate office may suddenly and quickly drop to the floor and kowtow to the CEO, or the women in a household may suddenly start to move in fast-motion, cleaning the house, while the men slowly yawn and loaf around. By showing the instruments of theater and how they can be manipulative — for example, the actor calling out “Cue the angry red spotlight!” before he shrieks with rage, or “Time for the gleeful violin” before dancing happily as the violinist joins him on stage, or visibly dabbing water on his eyes when he is supposed to cry . . . the audience can be entertained without being manipulated.
“The Brechtian style of acting is acting in…