Hello,
You should always clean any remaining thermal interface material from the core of the CPU and surface of the heatsink, before applying new thermal interface material.
The most effective and popular substance a lot of people use is isopropyl alcohol, which you can apparently purchase from the pharmacy. I can't seem to find it anywhere in stores, but on eBay. I use Akasa TIM clean (AK-TC) which is a citrus based solvent for cleaning heatsinks and CPUs. It works, but I don't like the citrussy smell and it seems oily, leaving me to doubt its evapourative-ness (yet, I don't know why I still use it).
As Sora said, just a very thin layer. It's tempting to just put a whole splodge on the core of the CPU and fasten the heatsink down tight, but it's actually most effective with a thinner layer. I spread a pea size onto the core using a small rectangular piece of plastic card.
Some suggest, as I do, to put some of the thermal compound onto the surface of the heatsink, spread it evenly using your finger (wearing a plastic glove or inside a plastic bag) and wipe away any excess compound (with your protected finger, or a lint free cloth). The idea is that the compound fills more of the microscopic imperfections on the heatsink surface, helping to create a more smoother and even surface for the core of the CPU to contact with. But you don't have to do this.
