A clean, dry surface is very important. After you clean the CPU surface, take a coffee filter and lightly get anything left over off of it. If you have a normal style CPU Heatsink, squeeze out a bit of paste about the size of a grain of rice right in the middle of the CPU. Seat your cooler on it, give it a very tiny twist clockwise and counterclockwise without taking the cooler off of the CPU and start tightening it down. If there are 4 screws to hold it down, tighten in an X pattern until snug. After you have them all torqued fairly evenly and snugged down good, you may want to give them another 1/8 of a turn.
Turn your computer on and open up whatever temp monitoring software you have.....RealTemp, Core Temp, etc. Let it idle for about 30 minutes and keep an eye on the temps. If the idle temps are good and you see no spikes in the temperature, go ahead and stress test it for 30 minutes to an hour. You want to stay right there with it in case it spikes up and you need to stop stressing it. After you have that done, check the bolts to make sure they are still very snug.