The process of taking the hook from (hopefully) the mouth of the fish. To do this with barbless hooks simply push the hooks in the opposite direction to the one they entered. For barbed hooks apply a little pressure on the top of the fly at the same time as pushing. This will disengage the barb and cause less damage to the fish.

Unhooking (oneself)
It may occasionally happen that you hook yourself. This will immediately teach you that barbless hooks are a good idea after all and secondly that it hurts.
To release a barbed hook from oneself, follow the principle above by pressing down and away as it is removed. For deeply hooked situations a length of strong monofilament is looped around the bend of the hook and the hook is pushed down and the monofilament pulled parallel to the entry would or slightly below. This will pull the hook out with minimal barb engagement.