I have formal training and a four-year acting degree from a fine arts school. I can address this question authoritatively.
The way I’ve always explained it — here on these boards, more than once, and elsewhere — is that acting is so simple that it’s incredibly difficult. At a professional level, it’s not really “pretending” the way a lay person understands it. The actor isn’t “putting on” emotions, in the sense of manufacturing them so the audience can see what the character is feeling. Rather, the experienced actor is just being. In one’s imagination, one adjusts one’s given circumstances, and then one simply is, pursuing whatever the character is pursuing, attempting to overcome whatever obstacles exist in the context of the scene, and the emotions that arise from this are supposed to occur naturally and organically.
But “just being,” for most people, is difficult and distracting. If I tell you to go get me that glass, you’ll walk across the room without thinking about it. However, if I tell you to walk across the room and I’ll watch how you walk, suddenly your body is a mass of twitches and anxiety. It’s bizarre how self-consciousness gets in the way of “just being,” but that’s what actors do. They simply “are” without acknowledgement that they’re being looked at, in a way that is simultaneously totally natural and completely unnatural.
And acting school helps develop this basic skill.
The technical part of acting is simple: What is your objective, and what are the tactics you use to achieve that objective? From these two factors, the character emerges. What the character wants, both in an overarching sense and from moment to moment in each scene, and how the character goes about attempting to secure those goals, are how the character is illustrated. One character may have a tendency to cajole, another may threaten. Another character may use both tactics, but have an excellent instinct for which is most effective in a given context; yet another character may also use both tactics, but be a poor strategist, deploying them at the wrong times.
My acting training was conducted along three general paths.
First was technical training — script and character analysis, primarily. One learns how to read deeply into a script to determine the character’s superobjective (the single overarching goal that motivates the character). Then one learns how to dissect the script moment by moment, splitting it into “beats” (n.b. the terminology differs from school to school, but the concept is the same) which mark where one mini-objective ends (in either success or failure) and the next mini-objective is launched. For each beat, the character’s tactics are analyzed. There shouldn’t be one obviously correct answer here, necessarily; the idea is to identify the range of tactics that the text supports, so the actor can try things, testing out a range of choices, during rehearsal.
There’s also the really technical training, which generally starts in classical texts where the impact is more obvious (e.g., note the spondaic foot that begins “Two households, both alike in dignity”). Has the playwright given the character more open vowels, more sibilants, longer or shorter sentences, etc.? If a characteristic quality of the dialog can be identified, can anything be concluded from such? The very best modern playwrights (Albee, Mamet, etc.) operate at a level where this kind of analysis may bear fruit, compared to someone like, say, Simon, so knowing how to dig into a text is a valuable skill, worth learning and practicing.
Second was exposure to a range of genre. The demands of Greek tragedy are very different from the demands of, say, Michael Frayn, or David Hare. One learns how to stretch and exercise a wider variety of acting muscles by taking on everything from Moliere to August Wilson. But the most interesting thing is, when one acquires this range of experience, one finds surprising commonalities, echoes of intention, between, say, Restoration comedy and Alan Ayckbourn. The skills transfer and translate. And by encouraging the student to attempt many different kinds of material, the actor’s instrument is tuned to a wider span of potential notes.
Third was simply repetition and practice. When I say “the actor’s instrument,” I mean that literally. It’s a common phrase in the field. One plays one’s body and voice very similarly to how a cellist or a pianist plays one’s physical instrument. First, one completes the technical work as described above, and one also, hopefully, has a variety of experience to draw on. Then, one gets into the play or the film, and one plays the notes — the tactics, beat by beat, in pursuit of the objectives. And by doing this over and over, both in the daily rehearsals for a specific piece and in the repetitive process of doing many pieces, one’s emotional availability and clarity naturally increases (assuming one is committed to the work).
A couple things to note here: First, this process is never done. One doesn’t graduate from acting school as a “finished” actor; one graduates, hopefully, “done enough” to become a professional and continue working on oneself. I guarantee you that if you asked, say, Al Pacino, if he went into The Irishman totally confident about everything he was going to do and came out of it having learned nothing, he would laugh at you. And second, different actors have varying levels of natural gifts in different areas. Some may come into the field with a high level of emotional availability, but need to learn analytical discipline. Whereas others may find the analysis easy, and need the repetition and practice to refine their emotional instrument.
Also, it must be acknowledged that some actors have no training, and succeed because their instincts carry them despite the lack of formal instruction. You see this occasionally when a pop or rock singer makes the leap from microphone to movies. David Bowie, for example, was an extremely interesting actor on screen, because he was confident enough to make clear choices and commit to them (i.e. “being”), but also creative enough to go beyond the usual choices of a conventionally trained actor. Of course, not every pop star who tried acting has been successful; Mick Jagger, for example, did a couple of movies, and is embarrassingly terrible every moment he’s on screen. So one may wonder if training is actually necessary, and the answer is, no, not always, but it’s certainly helpful for polishing an unrefined instrument.
This is just the beginning of an answer, but I hope it’s a useful overview.