solid and cured paste: scrape it off with a plastic straight edge, then use alcohol (isopropanol) and a lint free cloth (I use coffee filters) to remove any reside on the CPU and/or the cooler.
fresh liquidy paste: lint free cloth and alcohol. remove as much as you can and use a dampened cloth to remove residue. allow to dry
as always when working with components take grounding precautions.
Canned Grounding Rant-
shut down system and remove side panel. with the power cable plugged into the PSU touch a bare unpainted metal area of the case. (my favorite spot is an unpainted screw securing the PSU) once you have grounded yourself you can unplug the computers power cable from the PSU and can touch the system.
if you move your feet, or shuffle in your chair, plug in the cord, reground yourself and unplug again.
end canned rant-