I'm pretty sure none of us can imagine 4D. And 3D is quite literally seen as if it were 3D. How well you can cope with what's being seen is a different thing, some people just can't get used to the shuttering and somehow manage to lose the 3D effect. I personally find it amazing
Actually it's hella simple. They usually use two cameras to record, one for the left and one for the right eye. When the 3D movie is playing you have special glasses that block & unblock each eye so that you're constantly switching between seeing with the left and with the right eye. When the left eye is watching the projector shows what the left camera recorded, when the right eye is watching the projector shows what the right camera recorded.
So you practically end up seeing what you would see as if you were there, irl aka in 3D.