You will get many opinions on this. None are wrong.
The purpose of thermal grease is to fill in microscopic pits in the mating surfaces that can trap air.
Air is a very poor conductor.
Thermal grease is a better conductor, but nowhere near as good as the metal of the mating surfaces of the cpu and the cooler.
A common mistake is to apply too much grease, making it act as an insulator.
It is hard to use too little.
Apply only a small drop in the center of the cpu die.
When the cooler is installed, and tightened down, the drop will spread as intended.
It will spread even more when the cpu chip heats up.
Some grease, like AS5 will cure and become more effective over time. Perhaps 200 start/stop cycles.
But, don't get hung up on the method. Even a sub-optimal application will be effective enough.