I was trained in the Stanislavsky method. There is a lot of confusion about what "method acting" is, mostly due to the influence of Lee Strasberg's Actors Studio.
As I understand it, Strasberg emphasized emotion memory -- an actor "feeling it." This school of acting forgot that the purpose of acting is to communicate drama to an audience. In the '50s you might have seen two actors on the Actors Studio stage mumbling to themselves; their acting was "real" but it was not communicated to the audience. As a result, there have been actors who, when told by a director to do something, respond that they can't do it because they don't "feel it."
I can sympathize with these actors to a point. In my acting process I try to start slow in rehearsals and find a reality by pursuing objectives without worrying about results too early. Inevitably, by the third or fourth time I rehearse a scene, the director will become impatient and say something like, "You've got to be bigger" or "Pick up the pace." These results notes are annoying in the first few weeks because I KNOW I must be bigger, but I'm trying to get there from the inside out instead adopting superficial results.
One of the key epiphanies good actors make in their development is that acting is the imitation of what humans do, not what actors do. The beginner will approach a scene by trying to "act" -- that is, aping the results of other actors instead of finding the human reality.
This does not mean that one cannot learn excellent tips by watching master actors. I have learned much about enunciation, emphasizing words and elongating consonants by watching Alan Howard in the scene from Coriolanus on You Tube. But I can integrate these techniques into my acting because I have the foundation of my Stanislavsky training.
I'm not big on exercises. I get impatient with them because their purpose is not immediately tied to the purpose of theatre, communicating to an audience. I think it's better to learn by being in plays and solving problems, always with an eye to the ultimate purpose of performance.
I have learned through rehearsals that the quickest way to find the reality of the scene is to listen to the other actors and react to their words and actions. Just listen and react. Your reactions will take you to unexpected places and give you instant insight into what you are doing.
The biggest mistake actors make in this regard is that, until they are off book, they keep their nose in their book. Wrong! You must get your nose out of the book, look at the actor who is speaking and react. Even in audition, in a cold reading in which you have no idea what's going on, you should try to lift your nose from the page and look at the other actors. When you do this, your acting improves instantly. If you keep your nose in the book, you're not acting, you're reading along while other people act.
Another big problem beginning actors make: they do not stylize their acting. They make unnecessary movements, gestures, grimaces and vocalizations that clutter up their acting. I saw a rehearsal in the last year in which a young actress shifted her weight back and forth and fidgeted throughout like a restless child -- and she was playing the wise Portia in The Merchant of Venice! It did not occur to her that her every movement should be selected for the purpose of characterization.
Art is the selective recreation of reality. Actors must select their movements and eliminate the clutter. The Coriolanus scene I linked to above is highly stylized. Gestures are kept to a minimum and every movement is carefully chosen. The stillness of the actors is striking and powerful, but never alienating or unreal.
Once you are on firm ground in the rehearsal process, then you turn your focus to communicating to the audience. This is where technique comes in. This is where "feeling it" is not enough. The purpose of a play is to make the audience feel it, and here whatever works is good.
I was in a play recently in which I said, "I have been betrayed before by those I have known and loved." Now, I did not feel any great emotion inside myself when I said this. But I communicated emotion by choosing a brief pause before the words "and loved." That pause told the audience that the words did not come easily. That pause was the residue of being hurt in the past. The audience felt the emotion; all I did was coldly apply technique.
UPDATE: Other acting posts: