Buy a tube of thermal grease, preferably from Arctic Silver.
Get the old off using a paper towel dipped in PURE acetone or just dip it in rubbing alcohol with a high percentage of rubbing alcohol preferably more than 70%.
Rub it on the metal plate of the processor and the heat sinks
Then make sure it's dry on the metal plates.
Put a bit of thermal grease on the processor plate.
Spread it as evenly around as you can.
Mount on your heatsink and you're good to go.