As little as you can, yet cover the surface of the CPU. I apply it with a plastic toothpick or something similar (fingers are the best, get oil in the compound) then use a straight edge like a razor to skim the excess off. You don't scrape it clean otherwise there will be no compound left to conduct, you're just trying to fill in the small voids where the CPU surface otherwise would not contact the heat sink. I then place the heat sink over the CPU and give it a twist to ensure coverage in any gaps.
Ideally, when the heat sink is held on the CPU with moderate pressure (comparable to what the clips will do) you should be able to hold it up to a bright light and not see any light shining through the HS/CPU joint.