Put a little bit of isopropyl alcohol on the microfiber.

Clean all of the thermal paste residue from the CPU.

The new cooler usually comes with its own thermal paste, but if it doesn't or you want to add better thermal paste, clean the cooler the same way as the CPU.

Add a small amount of thermal paste at the center of the cooler.

Make sure that the surface of the CPU and cooler is dry before applying the thermal paste.