I was maybe... eight years old, or so. I was sitting at my window, looking outside. It was a sunny summer day. A block or two down the road, a boy was dribbling a basketball. I watched him and I noticed that I could hear the ball hitting the pavement just a little later than I could see it. I knew this was because sound travels more slowly than light; I had read about it in one of my books about weather, which explained how you could tell how far away a thunderstorm was by counting the seconds between the lightning and the thunder.
Then I thought to myself: "If I were him, I would hear and see the ball hitting the pavement at the same time." And I remember making the mental switch to another perspective, standing on a driveway, bouncing a basketball, perhaps looking up at a house down the way where a little girl was looking out her window. I remember thinking that people's worlds must all be slightly different from each other, depending on who they were and where they were. I remember thinking that each person had their own separate world, and it almost made me dizzy.
That was around the time that I realized it was possible to flip one's perspective, mentally, and figure out what someone else might be thinking. Most kids learn theory of mind around four years old or so, and I'm sure I'd been figuring it out myself for some time before that (I remember thining "My mother is wrong" around age six, so I must have known it was possible for two people to think two different things at that age), but I do think I might have been a little late in figuring out the mental switch involved in theory of mind. Mental switching in general is hard for me.
Autistic people often have a hard time with thinking about two or more people's perspectives at once. It's mental multi-tasking that's hard to juggle for people who have a hard time multi-tasking; multi-tasking requires switching from one task to another very rapidly, and many autistics have trouble switching at all. So it's a difficult puzzle for us to learn. It takes us longer, like it takes a dyslexic person longer to learn to read.
Not every autistic person is delayed in learning theory of mind--in fact, some are so extremely sensitive to others' minds that they lose themselves in others' emotions--but I'm one of the ones who tended to ignore other people and focus on information. That's probably why I needed to use the idea of sound and light speeds as a bridge to think about the differences between human minds; it was easier to think about science than about multiple perspectives.
If you, or a younger autistic friend, have trouble with theory of mind, maybe it's easier to think about it as a logic puzzle than to think about it as a social skill. Maybe we could teach autistic children how to figure out what somebody else is thinking, by presenting it as a logic puzzle.
Start with visual perspectives; those are easiest. Sit on opposite sides of a table with a partner; put up a divider between you, and hide something on one side of the divider so that only one of you can see it. Observe how you can see the object only if it is on your side of the divider; then demonstrate that if you were on the other side of the divider, you could not see it. You could talk about what you know versus what your partner knows. That is the simplest type of theory of mind--two perspectives on the same situation, with a setup you can visualize. Practice the mental switching; place yourself mentally in the other person's position, and compare where you are to that mental image.
In most interpersonal ToM puzzles, the divider isn't physical. The "divider" is the fact that two people's minds operate independently of each other. So, in order to solve the puzzle, one has to put oneself mentally on the other side of the divider, and then compare that other person's perspective to one's own.
Forming the mental image of the other person's perspective is the first step of theory of mind. While you are doing that, just forget your own perspective for the time being; remembering it will distract you. Form a good picture of the other person's perspective, and remember it. Then, take your own perspective and compare. There will probably be differences. For example, take the situation of giving someone a present. You want to give them something that will make them happy. The instinctive solution is to find something you associate with happiness and give that to them, but that doesn't use theory of mind, and could result in mistakes. Instead, you have to put yourself in their place--make the mental switch--and think about what THEY might associate with happiness. So, perhaps they like drawing, and you do not. You don't associate a set of colored pencils with happiness, but they do. If you want to cheer them up, giving them colored pencils would be a good choice even though colored pencils would not make you happy if you got them.
This is still pretty simple, and I'm sure most autistic adults figured out simple ToM puzzles long ago, just like I did. But the beauty of it is this: The same principles can be applied to really complicated ToM puzzles, too, with multiple people's perspectives in them. Once you know the trick of mentally switching your perspectives to another person's mind-set, you can figure out the way they might see your actions and the actions of those around them; and you can coordinate your perspective with other people's. In the end, if you are good, you should be able to figure out second-order ("What she thinks I am thinking"), third-order ("What he believes I think she must want"), and multiple perspective ("He and she disagree about my beliefs") problems.
But it is really just a logic puzzle. Don't be intimidated by it; it's just a matter of practice. Too many professionals think of "theory of mind" as some magical thing that NTs can do and we can't; in fact, NTs just have sort of a rough, intuitive grasp of it, whereas autistic people, who study it explicitly, often get to be better at theory of mind when NT intuition starts to fail. For example, we tend to understand that people think differently, because we learn pretty early on that we think differently from other people. When an NT switches perspectives with another NT, they can usually just pretend that the other person is more or less just like themselves. But we can't do that--we have to take into account mental differences. When we learn to switch perspectives, late as we may be at learning it, we by definition have to learn to switch into the frame of mind of another person who is different from ourselves.
I think that's why many of us are good at communicating with animals--it's not some kind of psychic link; it's just the way that we tend to understand that animals are who they are, instead of assuming they are just like humans. We might also be pretty good at understanding people who are unusual to us in some way, perhaps those from different cultures, or those with disabilities other than autism, or those who are much older or younger than ourselves. It's not natural talent; it's practice.
NTs might never have to learn how to switch perspectives in any way but the superficial, intuitive style they learn at about four years old, because they don't meet too many people who think in ways very unlike the way they think. But autistic people spend every day interacting with people who don't think the way we do. We study theory of mind like we study math. When professionals say we have "defective theory of mind", I think they had better check their own theory of mind, because while we might be slower at learning it and slower to apply it "in the field", we're perfectly capable of figuring out what the view might be like through somebody else's eyes.