When installing a new CPU what is applied directly to the CPU?

Before installing your Heatsink and Fan to the processor you should be applying Thermal Paste. There are several hundred versions on the market and any good computer store will have ooddles of the stuff.

Ideally don't spend less that €10 on a tube. If its cheaper than €10 its generally useless. In some case, some of the more expensive thermal pastes contain an adhesive to ensure the heatsink sits better on the processor.