The goal of the different schools of acting is to give the actors tools by which they can access their own emotions in the unconscious mind. Since the unconscious mind can't be controlled directly, students are involved in various exercises that are designed to evoke specific emotional correlates.

If I, a non-actor, was to attempt to describe the basic theme of the leading contemporary schools it would be this:

Adler is built upon Imagination.
Meisner is built upon Immediate Experience.
Strasberg is built upon Sense Memory.
British is built upon Observation.

The Meisner system seems to produce actors that pay attention to their partner better. Some of the basic Meisner exercises include the YES/NO and various repetition and back-and-forth exercises that tend to 'bond' the actors together. "Acting is living life truthfully under imaginary circumstances". "The emotional life of a scene is a river and the words are the boats".

The Strasberg system or METHOD system tends to produce actors that are a bit more tightly wound. The system is based on SENSE MEMORY which is the process of recalling all of the attributes of an object, and EMOTIONAL MEMORY which is the process of recalling significant events and situations from the actor's past.

This produces the best actors for Blue Screen and effects performances but often at the expense of the actor's mental health. Stella Adler once said about Lee that "he would push people into spaces that they should not go without a licensed therapist present." Strasberg would often tell actors that they should get some therapy. Personally I feel the best improv exercises use sense memory. It catapults you into a sense of belief. PRIVACY IN PUBLIC. "Visualize a real situation in your own life and do your lines within that frame of mind."

Stella Adler gives us the process of action verbs and is based on imagination as being the best motivation for a good performance. The imagination is very powerful in the presence of a director who loves to tell stories. " Get the verb of it, don't worry about the emotional thread".

The Britishapproach to acting is an odd one. Not that it doesn't generate spectacular performances or consummate actors but rather is based on the actual achievement of acting. Rather than becoming the character emotionally or mentally, the British system actually emulates a character by adopting all of the physical traits and characteristics.

Like I said, there's probably not a practitioner of any of these schools that would agree with my rather shoddy generalities so do your own research or read Judith Weston's book, Acting for Directors.