If the pails have handles, turn the stack upside down with the openings facing the ground and place a foot through the handle of the bucket closest to the ground. Grab the topmost pail by the rim, and pull up, using both the back muscles and the arms.
For stubborn cases, put the stack of pails in the bathtub and run hot water over the surface of the bottom bucket, rotating the stack so that hot water covers its entire outside surface. Pry the pails apart by placing the stack upside down, bracing it with your foot on the bottom handle and pulling upwards on the bucket that was rinsed with warm water. If there is no handle, secure the stack by squeezing it between your calves. The hot water heats the air in the pocket between the buckets, thereby stabilizing the air pressure on either side of the pail, making it easier to pry them apart.