Apply the paste on the CPU's very carefully, you don't want certain thermal pastes on electrical circuits.

Your paste needs to be distributed evenly on the whole metal cap of the CPU.

Reverse engineer this guide to put the laptop back together.

Let the paste settle in by letting the computer run for a few consecutive hours.

Run a temperature monitor software to check if your application has been effective or not. After a day or two, you may want to stress-test it by running some high end application all together and monitor the temperature.