Remove the CPU from the socket. Wipe off as much as you can with a paper towel. Then use a Q-tip and rubbing alcohol to remove the rest. Keep using clean Q-tips though and fresh dip of rubbing alcohol. DON'T pour it, just dip the Q-tip in and then wipe the CPU with it. You might have to run a bit hard if your thermal paste is kinda dry. Keep doing it, fresh stuff when the current gets dirty and it'll come off.
Then do a clean one at the very end to shine it up. Then reapply new paste, reinstall CPU into socket, reseat heatsink, and let 'er rip