Filleting a whole (gutted) fish is not hard, though it does take practice. Here’s what to do, from New York author and fish expert Paul Greenberg.
Note: If you are skinning the fillets, do it with a knife that’s duller than a filleting knife. To remove the skin as easily as possible, you don’t want the blade to cut through it as you work.
Lay the fish on a cutting board with the dorsal fins facing you. (The fish should be scaled if you plan to eat the skin, unscaled if you’re going to skin the fillet.) Use a thin, flexible, sharp knife to make an incision parallel to, and slightly behind, the fish’s collar bone, keeping the head attached.
Starting at the top (dorsal) end of the first cut, make another incision perpendicular to the collar, along the spine, cutting through the skin from head to tail.
Run the blade as close to the ribs as you can, gradually freeing the flesh from the rack (bones/skeleton in the body). If you are where you should be, you’ll hear a washboard sound as the blade runs along the bones. An expert can remove the fillet in one or two cuts. It may take half a dozen for a first-timer.
Once the fillet is nearly free of the bones, cut through the belly skin; transfer the fillet to a plate.
Turn over the fish and repeat with the remaining fillet. (This will be harder to remove than the first side because the fish is no longer lying flat, and also because right-handed and left-handed cooks always have a dominant side that works better. Don’t be too hard on yourself if the second fillet doesn’t look as good or if you leave some flesh on the bone.)
To skin the fillet, lay it flesh side up on the cutting board. Use a somewhat duller knife to cut a nick about 1 inch from the tail end, then insert the knife at a 45-degree angle. Holding tight to the tail end of the fillet, slide the knife blade under the fillet. Move the skin back and forth until the fillet is released.