I personally spread a little on the center of the Heatsink (a little larger than the core), rub it in very well, and then remove all the excess. My thought is that since I don't have a perfectly lapped HS, the Artic Silver (or whatever your using) will fill in the voids to some extent. The hope is that there is more resulting surface area when the heatsink is finally applied. The PROPER thing to do would simply to lap the heatsink so it is totally smooth.
I WOULD NOT spread a layer of thermal paste over the 'sink and run it that way. It simply would do nothing other than cause unnecessary mess.
I apply a layer of thermal paste (as thin as possible) to the CPU core then and install. I generally use an old credit card as an aplicator to try to get a really thin and even layer across the core.