First, unscrew the six screws that are holding down the fan and heat sink with a Philips #1 screwdriver. Then use a Phillips #1 to remove the single screw near the bottom of the heat sink.
Six Silver Chrome 5.8mm Phillips #1 screws
One 5.8mm Phillips #1 screw
Remove the four screws that are holding down the CPU (the four to the top left that form a rectangle in this image) first. Unscrew them in an X pattern (eg. top left screw, bottom right screw, top right screw, bottom left screw) to minimize risk of harming CPU.
When installing the new heat sink, do not forget to replace the thermal paste underneath the heat sink. See iFixit's Applying Thermal Paste guide for further instructions.