A number of different special unarmed moves (eg, Ranger Takedown) require a "power attack" to actually activate them. How the bloody heck do you do a power attack on the PC? Is there any way to do one in VATS? If there is, I've never seen a prompt for it...

Hold down attack button to launch power attack. While moving in different directions will make different power attacks. Works for both unarmed and melee.

Also when you have enough unarmed/melee skill VATS will show new button prompts for special attacks.

Thanks Pistolero, that's what I was looking for. On PC, I assume the attack button is left click on the mouse.

Tojka, despite having Unarmed at 100, I've never seen a prompt in VATS for 'Ranger Takedown' or 'Scribe Counter'. Can anyone confirm that these aren't available in VATS, or tell me how to access them from VATS?

I don't think you can use those attacks in VATS (never played unarmed myself) but there should be other special attacks available. The Vault lists these: http://fallout.wikia.com/wiki/Unarmed#V.A.T.S_Special_Attacks

Yeah, I've been trained by that one NCR Ranger and one other character to do some crazy move but could never figure out how to do it. I honestly think these power attacks were by far one of the dumbest things added to Fallout: New Vegas. They honestly don't add anything and are fairly difficult to pull off.