It's been about 10 years since I built a PC, but I always did the following, and never had any cooling issues - in fact, I got quite good overclocking results:

Using plastic gloves (or just put a plastic bag over your hand) spread a REALLY thin layer over the cooler using your finger. This is simply just to fill any small grooves in the coolers surface. If you lap your cooler you don't need to do this.

Using a credit card spread a layer around 1mm thick on CPU, the main thing here is to just try and cover the whole area of the CPU that comes into contact with the cooler.

The most important thing is not to fret too much about this. Once you've put it all together, run a stress test and keep an eye on the CPU temp, if it goes too high, just clean the paste off and try again :)