This is my rule of thumb:
Put about a grain of rice sized bit on there.
I wouldn't use a credit card or something like that. They are too inflexible and don't make it as easy. If you can find one, get a pack of matches that has a glossy exterior cover and use that side to do it. Or, find something made of a thinner, more-flexible plastic than a credit card. It will let you more easily drag a flat surface that will allow it to spread more evenly.
Get as thin of a layer as possible of thermal paste across the entire surface of the CPU. Thermal paste, as has been said by others, is made to fill in the microgaps between the CPU heatshields and the cooler where there are micro scratches. Air is the WORST thermal conductor. Hence, you want a layer of thermal paste that completely covers the surface of the CPU while being as thin as possible so that the CPU and heatsink make as much direct contact as possible.
I also will use whatever spreading tool I have to drag the paste across the CPU both left and right. As soon as I have it covered one direction, I then go up and down with it.
If you can't cover the entire CPU with what you applied, put a very small amount on (just a small dot) and spread that to the open spots on the CPU. Do that until you cover the CPU with the minimum possible.
I used to apply thermal paste in somewhat more quantity, and it made my temps higher. Now doing this, my temps have dropped about 5-8C. So, it can make a big difference.
Good luck.