Unscrew the heatsink screws in the order shown in the first photo, and gently lift up on the heatsink to seperate it from the CPU/GPU dies.

Using isopropyl alcohol wipes or isopropyl alcohol on a Q-tip, 90% or higher (if you use 70%, make sure to not get the alcohol on the motherboard, and make sure to thoroughly dry off CPU/GPU dies, surrounding areas, and cooler with a microfiber towel before applying paste. Also, if there is dust or cats in the cooler, remove them.

If the fans and/or vents are full of fluff, use an air dryer and a paintbrush or toothbrush to remove all the dust.