In my dojo, they are taught to perform takedowns with good control. Once they understand how to do the takedowns, then they are taught how to fall correctly.
I'm the unorthodox one out the the instructors, though, since I prefer to let them learn how to fall first, and then work the takedowns.
I'll start by taking the jigsaw mats (made of foam rubber), and lock a bunch of pieces together, and start the students out by having them lie down on their backs, with their feet in the air, chins tucked in.
They start by opening up their palms, and slapping the palms and the forearms on the mat many times, so that they can get used to the idea of maximizing surface area.
Once they're accustomed to that, I'll have them start from a sitting position, and have them roll backwards, with their chins tucked in, and have them spread out their arms, and repeat the above slapping motion, so that they can now apply the concept of spreading out the impact over a larger surface area.
Once they're comfortable with the sitting position, I'll start them out in a squatting position, and then have them learn how to spread out the impact while falling sideways.
Usually, that's more than enough for a first lesson, and the next morning, I get people telling me that they're having a harder time gripping that cup of coffee in the morning (first timers always get the shakes). Still, I haven't had anyone say that they hated the knowledge.
Once they're comfortable with all of the above drills, then I'll have them partake in some gentle takedowns, and some gentle throws on the mats, so that they can get the idea of sticking the arm(s) out when they are engaged in a fall.
I always try to partner people with equivalently sized / strength folks, but once in a while, there's that really big fellow, who weighs 280 lbs that I can't let the others try, so of course, I'll be his partner. I don't mind letting him throw other people, since everyone knows him as the gentle giant (and one heck of a good fellow, too), but you do need a certain minimum amount of strength to work safely with him.