Summarize:

This method is ideal for round-bodied fish, such as trout, tuna, and salmon. Try to get as close to the fish as possible. Leave the tail on for now. Run a fish scaler down the side, back, and belly of the fish. Always go against the scales, from the tail end towards the head. If you do not have a fish scaler, you can use the edge of a spoon or the back/top of a knife. As you are "raking" the fish, the scales will peel off. Keep raking until no more scales peel off.  Rinse the fish, if necessary, to get rid of any excess scales. This may take a while for fish that have tiny scales. De-scaling a fish can be messy. Consider working on top of a newspaper. This way, you can just crumple up the mess and toss it out when you are done. You will be cutting into the fish at a downward angle. Always cut from just behind the fin towards the head, but do not cut through the spine. These are the three cuts you will have to make:  Cut from behind the side fin down to the gills. Flip the fish over and repeat the same cut on the other side. Turn the fish onto its back. from the behind two underside/pectoral fins down to the throat. Grab the fish by the head with one hand and the body with the other. Quickly twist and snap the head off. Pull away any guts that come with it and discard them as well. Slip the tip of the knife into the "vent" or anal opening. Cut towards the head. Keep the cut shallow so that you don't pierce the guts. If you pierce them, you might taint the meat. Turn the fish onto its back and spread it open, like a book or hot dog bun. Pull the guts out and discard them. If you see a kidney near the backbone, use a spoon to scrape it out. Run the tip of your knife down the center of the fish, right where the backbone would be. This pierces the membrane and exposes the bloodline. Use a stiff-bristled brush to clean out the mess. You want to remove the bloodline because it can give the fish a bitter taste after you cook it. Gently massage the flesh to get rid of any guts or blood. Run your finger down the center of the fish, where the bloodline was. Lay the fish down on its side, and spread it open. Cut the vent out at an angle. Flip the fish over, and cut the other side of the vent out. Start at the tail. Hold the knife so that the blade is almost parallel to the cutting board, but at a slight downward angle. Peel the skin up and slide the blade between the skin and the flesh. Carefully saw the flesh away from the skin. It helps to pull the skin up and towards you as you go. Some fish, especially bottom-dwelling fish, should be skinned. Other fish, such as salmon and trout, are often cook with their skin on.
Lay the fish down on a cutting board. Trim all the fins off using a pair of scissors. Remove the scales. Make three cuts around the head. Snap the head off and discard it. Cut the fish's belly open. Remove the guts. Cut through the spinal membrane and remove the bloodline. Rinse the fish under cold water. Cut the "vent" or anal opening out. Consider skinning the fish.