How to clean the rubbery skin from monkfish before cooking?
This video posted by Rogers Powel shows the technique very clearly.


Place place the filet skin side down.
Grasp the tail end, and slip your thin, flexible knife into the filet by the tail end, scraping against the skin, cutting down the length of the fish.  
Turn the fish over, and inspect.  If any pieces remain, removing them is similar to removing the silverskin from a pork or beef tenderloin.  Slip your knife under the end of the remnant, pulling the blade up against the skin and cutting down its length to remove.


I recommend watching this video or others, because the technique is easier to see than understand from a written description.