Cleaning your chip first
If you’re installing a new heatsink before you even had a heatsink on you CPU, then there is no need to do this. But in the case of putting a new one on, or changing a video card cooler, then you must clean your chip first.
For this, most used is Isopropyl Alcohol, Acetone, or a solution called ArctiClean. For using the cleaners, use non-linty cloth or Q-Tips (cotton swabs). Q-Tips are great where they're small and easy to get where you want, plus you can also see exactly what you are doing.

For Isopropyl Alcohol, the higher the percentage the better. 70% is not bad, 90% or higher is the most ideal. The reason; the higher the percentage, the quicker it will evaporate and the less residue it will leave. 99% will leave almost zero residue.
Note: Never use any oil-based cleaners, as oil will ruin your coolers performance because it adds an oil layer through which heat travels slowly.
When you have your cleaner, dip your cloth/Q-Tip in, then gently rube the surface of the chip until all the old paste is gone. You will probably have to do this more than once to get it nice and clean. It is usually a good idea to use a credit card to scrape most of the old TIM off, and then use the cleaners.
The exact same process is used to clean the CPU/GPU. Just be careful if you're cleaning the CPU out of it’s socket. If you push to hard on it, you might bend a pin.
Note: Make sure you do not touch the surface of the chip with your bare finger, as your skin has natural oils on it as well.
To remove thermal pads, use a credit card or some other plastic object (do not use a metal object as it could scratch the cooler's base). Then follow the same procedure as stated above. You want to make sure all of the old paste or thermal pad is gone, otherwise it can affect performance of the cooler.