Brief History
Stanislovski developed this "science" of acting in Russia during the turn of the last century. Strasberg was greatly influenced by the works of the Moscow Arts Theater, of which Stanislovski was heavily involved, and decided to bring these teachings back to the United States. Since Strasberg began "spreading the word" the world of acting has never been the same.

The Method
Method acting makes demands of an actor to actually feel the emotions as the character would feel them. In essence The Method is the ability to delve into ones own past and conjure several experiences at once. Through the use of various exercises the actor discovers what emotional ties he/she has to objects, personal experiences and environmental conditions. The actor takes these various conditions, combines them, re-experiences them and becomes the character. The Method can be thought of emotional juggling in a sense because, basically, that is what the actor is doing. Of course, the actor has much more to consider once the emotion is in place.

example
Lets say a character is angry, depressed and drunk while delivering a line. Cold, as an overall effect, can deliver anger to some. The actor would then find an object or event that gave them the feeling of depression, such as a important personal memento that they may have lost or a failed relationship. Being drunk is a sense memory just like any other emotion, the actor simply induces that state by reliving it.