Ok, the top of the intel chip is actually a heart spreader. As such, its purpose is to transfer/dissipate the heat over its entire surface area to the surface that it makes contact with (the heatsink). For better or for worse, even the accurately machined surfaces of the heatsink and heat spreader do not make good enough physical contact to transfer the heat well, so a "thermal interface material" is needed, as you already know...
So-called thermal greases are just metal powder suspended in silicone oil. Fine silver particles transfer heat very well, but also go for electrical conductivity. Aluminum and/or Zinc oxides do not introduce significant electrical conductivity, but do not transfer heat as well. These are the typical white greases. I don't have a strong preference, and use whichever I come across first.
In any case, application of any thermal paste is pretty straightforward. For a small area, you may put a small dab of it in the center of one contact surface and firmly press the other surface straight down on it, taking care to not spin either contact surface. This applies to the Athlon XP's, for one.
For a larger contact surface, you'll have better results doing a bit of the spreading yourself. Put a reasonable amount of grease on the surface, and use a new razor blade to spread it as evenly as you can. How much to use varies by product a bit, so either follow the manufacturer's instructions, or add it incrementally. If you mess it up, wipe both surfaces clean with an alcohol swab, sold by the hundreds for cheap at any pharmacy.
Once you have a thin layer, as thin as you can get it without exposing the metal surface, then you ideally would "rock" the second surface on top of it. What I mean by this is you line up one edge, with the opposite one elevated, then bring the opposite one to rest. This way, air bubbles can be minimized. If you just drop the heatsink on top, it will trap air bubbles. Think of this like applying laminate on paper--you start from one edge, and push out the air as you continue to the other edge.
Now that it's in place, secure it with as little movement as possible, then push straight down as hard as the components can handle reasonably. I prefer to do this before installing the motherboard on a hard table or desk so the motherboard doesn't flex too much. It goes without saying that you don't want to break anything by pushing too hard!
And voila, that's it! Same procedure for a GPU, CPU, memory module, chipset, etc...
Good luck!
... Just here to help! If I've been of assistance please encourage me to carry on by letting me know :-)