Turn the stuck buckets upside down so the open end is facing the ground. Set them on the ground.
Put your foot through the opening of the bucket handle closest to the ground.
Grasp the bucket closest to you by the rim. Pull upwards, keeping your foot through the handle of the bottom bucket until the top bucket releases.
If the buckets are still stuck together, run hot water over the outermost stuck bucket for 30 to 60 seconds. Repeat the first three steps to pry the buckets apart.