When filleting a fish, what you really want to do is, well, whenever you do anything, whenever you're doing any kind of prep, whatever the meat, always make sure that you have a really nice sharp knife. A sharp knife is a safe knife. I know we've heard that before, but it's very very true, because the sharper the knife, the less pressure you're going to have to apply. As soon as you start applying pressure to a knife, that's when you can slip and you can hurt yourself, or just lose meat. Really make sure that your knife is nice and sharp.
The next thing you want to do is when you have a fish, whether it's round or flat (so round like snapper, salmon, stripe bass, and any of those fish that are actually round and have two sides, or something like a flounder that's flat that has two sides but you can get four fillets out, either way), what you want to do is you want to make sure that you have a starting point and an ending point for your fillet or your cut. What you can do is you can take your knife and draw a line around the back of its head and down behind the gills. It's actually a little bone structure that you can follow. You can just draw a line there and then come down to the tail and draw another line. By drawing those two lines, you've kind of created your points A and B.
You can now then take your knife, and if it's a round fish you would come up from actually up by the middle fin which is kind of up by the spine on the back, like a shark fin almost. Run along there, and go from your point A to B. If you're dealing with something like a flounder or a flat fish, you could even start in the middle of the fillet and just come down, almost like splitting a chicken. Just coming right down the middle to the spine and then opening it up like a book.
Once you actually are starting to fillet, whatever you do, always make sure that you use nice clean strokes. If you're doing a short, sawing motion, you could really shred up the meat and lose a lot of product. The fillet knife, or the boning knife, is actually a great tool for that, because what you can do now is you can actually bend the knife a little bit and use it to just glide the teeth across the bones. Literally, just kind of releasing the meat off the bone. So you don't have to saw. Just nice clean strokes, and that fillet should open up for you.
Once your fillet has been released off the spine, you can actually take the knife and just kind of clear the skin off from the inside and release that entire fillet from the fish.