With the eyed (dark) side of the flatfish up, use a flexible boning knife to make a cut along the spine from the gills to the tail.
Slide the blade between backbone and flesh, lifting the fillet away from the bone. Remove the second fillet in the same manner.
Turn the fish over: repeat step 2.
To skin, grasp fillet by the tail end, skin side down. Holding the knife at a slight angle, cut the meat free.