To remove the heat sink, pull it away from the fan and up.

You’ll probably need to wiggle it around a bit, but it should come out easily.

Be careful, however; there will be thermal paste in the middle of the bottom, where it connected to the CPU. If you’re putting in a new heat sink, I recommend cleaning off the CPU and applying a new layer of thermal paste.

Done! The heat sink is out. Check the conclusion for a little information on putting it back in.