The first and most important step in breaking down salmon is to check the salmon you are purchasing for freshness and quality. When checking a fish for freshness, look for clear eyes and pink under the gills. Smelling the fish is another way to check for freshness, it should not smell strong. Fresh fish will also feel firm to the touch.
Once you have your fish then you are ready to begin the butchering process. When breaking down salmon, you will need fish tweezers for pulling out bones, a sharpening steel for keeping your knife sharp, a very sharp knife, a cutting board, two towels to prevent slippage, gloves to prevent cross contamination, and an apron. After gathering the needed items get started by putting on your apron and gloves. Next place a towel on your cutting board, and then place the fish on top of the towel. This is to prevent the fish from slipping to help avoid cutting yourself. Use your sharpening steel and sharpen your knife, the sharper the knife the easier it will be to clean the fish.
Make an incision across the salmon underneath the fin next to the head until you feel bone. At the tail end of the fish make an incision across the fish right in front of the tail. Place a towel on top for the fish to prevent it from slipping. Then keeping your knife at an angle of 8 or 9 degrees to the cutting board, cut through the salmon along the bones from the tail end of the fish to where you made the incision below the gill. As you cut, you will hear the knife cutting through the bones. You want to get as near to the backbone of the fish as possible so not to waste meat.
Next the belly has to be removed from the filet. Make an incision between the belly and the filet with an angle that is against the contour of the fish. Cut the belly from the filet being as gentle as possible to avoid damaging the filet. Roll the belly out as you cut and repeat this until it has been removed.
Now you are ready for the final steps of butchering the salmon. Look and feel for pin bones, there should be about 20 of them, in the filet. Use the fish tweezers to pull the bones out. Feel the entire fish to make sure no bones were missed. Cut off any excess fat remaining on the filet. To remove the skin from your filet, sharpen your knife again and starting at the tail end make a cut until you reach the skin. Run the knife between the skin and the filet using the cutting board and towel to avoid the fish slipping and injuring. Once the skin is removed from the salmon, it is ready to be cut into portions. The average size for a portion of salmon is about 6 ounces. Using your hand as a guide, a 6 ounce portion is about the width of 4 fingers.