No problem
Get it nice and hot - either play a video game or watch a movie for a while. The reason for this is so you don't damage the CPU by trying to pry the heatsink from the CPU and accidentally rip off the spreader. Twist the heatsink a little bit until it comes a little loose, then you can more easily take off the heatsink. You'll save your wrist and your processor
You can use a paper towel or q-tips with alcohol to take off the paste. Depending on your system, the heatsink on the CPU might be mounted a special way - either by a stock cooler which is usually easier to take off or a third party heatsink which may require a screw driver.