No fingers were cut while bringing you this how to.
Before you do anything else rinse the fish in cold water. Then cut off the fins as seen above. The easiest way to do this is to trace around the cartilage. Keep them if you are making stock other wise — into the trash.
Begin the cut at the base of the tail and lay the blade on the spine. You are going to trace the knife blade up against the spine of the fish keeping it parallel to the cutting board.
Halfway through the fish take the knife and score down from the top. Use the top fin to judge where to make the first incision.
Using the knife blade separate the flesh from bone by working downward while holding the fillet up. By tracing the blade across the bones the flesh will lift away.
After working around the rib cage slice the remaining meat away from fish body.
There will be a small piece of fish remaining on the skeleton. Score against the bone to remove it. I like to use this part to flavor stocks and sauces.
Above are the two fillets plus meat tenders and carcass.