Interestingly, this technique is often called throat singing, because it typically occurs with a style of singing that does begin in the throat. But the overtones themselves are "singled out" by the shape of your tongue, which is why it sounds so much like a varietal RearrrearrrRRRRearrrr effect. The "throat" part of throat singing is the rough "frog" and grinding sounds you hear in Tuva (for example), which is done to provide richer overtones for singling out with the tongue.

I saw an illustrated guide of how to do it, but it was so long ago I probably won't find it again. It's basically a lot like how you pronounce the R sound, except that your tongue takes on a bit of an S wave shape. If you look at a referee's whistle, you can get a fairly good idea what shape it is that you are forming inside your mouth. The shape of the whistle is to emphasize a specific frequency in the hiss noise made by blowing into it. Polyphonic overtone singing is pretty much exactly the same thing, but using voice instead of hiss to generate the complex tones.

And just like learning to whistle, at first you'll sound like a raving lunatic and maybe even come close to passing out from hyperventilating. But once you begin finding the ideal tongue placements for a pitch, you'll very rapidly learn more, and it'll be exactly as automatic as after you learn to whistle. They're very very similar things to do, and the difficulty is identical.

If you are tongue tied (as I am) you probably won't ever be able to do it right. But you should be able to coax out at least a bit of overtone.

Now go out and try it, and enjoy knowing your neighbours will be forever terrified of you.