Using a pair of blunt tweezers, push on the tabs of the small white connector to separate it from the motherboard.
The entire bottom casing should lift with no resistance. If there is too much resistance, verify you removed all the screws, and run the plastic spudger tool around the face-plate again.
Once you separate the heat-sink from the motherboard, you will need to clean and re-apply thermal compound. Do not proceed unless you are prepared and you have the necessary materials.
Using both hands, gently lift the heat-sink and fan components from the motherboard.
Old thermal compound can dry up and adhere the heat-sink to the motherboard like glue. This may make removing the fan and heat-sink difficult.
Do not re-seat the fan and heat-sink without cleaning and re-applying the thermal compound. For more information, please refer to this guide.