Thermal pads and grease are applied for one-time use. Whenever you replace the heatsink, you should clean it all off and re-apply it fresh.
Which implies you shouldn't take the heatsink off if you don't have fresh thermal compound to put back on it.
I've always used rubbing alcohol (isopropanol) for cleaning off the old gunk. You probably have some somewhere in the house already. If not, any drug store should have it.
It is easier to apply the new compound to the CPU. If your CPU has an
exposed core, apply a thin and even layer to the top of the core only. If it has a
metal heat spreader, coat evenly the entire surface. Less is more -- the thinner the layer of thermal compound, the better.
