This video will teach you one of many techniques for butchering a whole salmon, or any "symmetrical fish," as opposed to a flat fish like halibut or sole.
In this video I state that I like to brine the fish briefly in a "5% brine." The brining process will keep the salmon moist during cooking. To calculate a 5% brine, weigh out enough filtered water to cover the finished salmon fillets. Multiply the weight of the water by .05 which will give you the amount of salt needed to achieve a 5% brine. For example, if you need 1,000g of water to cover your salmon fillets, simply multiply 1,000g X .05 = 50g of salt. Disperse 50g of salt into your water, which will result in a 5% brine.
Brine salmon for 20-60 minutes, rinse under a gentle stream of cold, running water and allow to drain.