Set salmon down with the head end pointing right. Trim half an inch off of the head end and all of the salmon's fins. Insert a sharp knife, horizontally, into the head-end, just above the column of bones running down the middle of the fish. With your knife angled downward, carefully cut along those bones toward the tail, loosening the fillet from the bones. Now lift the fillet up and very carefully cut it away from the rib cage and tail.
Turn the fish over and remove the other fillet as you did the first. Carefully trim away any rib bones still attached to the flesh of the salmon fillets.
Salmon fillets have small pin bones embedded in the flesh - to remove, run your finger, lengthwise, down the upper middle of the flesh. Grab the bones (that should pop up) with tweezers and pull them out. Leave the boneless fillets whole, or cut them into single serving portions.