One simple way to cook salmon is to pan-sear fillets in a hot pan coated with olive oil and butter. Sear the skin side for a few minutes, then flip and finish cooking on the other side. Another option is to roast the salmon in the oven until cooked through.
To pan-sear salmon fillets, pat dry the fillets and season generously with salt and pepper. Coat a large skillet with olive oil, add a few tablespoons of butter for flavor, and place over high heat. When the oil is very hot, place the salmon skin-side down in the skillet. Press down gently with a spatula, and let the salmon cook, without moving it, until the sides are cooked halfway up the fillets and the fish slides easily across the pan. Flip over carefully and continue to cook until the sides of the salmon are fully cooked. You can take it off the heat then for medium-rare, or continue for a few minutes more if you prefer the salmon more well-done.
To bake salmon fillets, preheat the oven to 350 degrees Fahrenheit. Drizzle olive oil over the fillets, and season with salt and pepper. Place the salmon on a non-stick baking sheet and bake for about 12 to 15 minutes, until the salmon is cooked through. For extra-moist salmon, cover the fillets in a flavorful marinade and wrap tightly in foil. Bake the salmon at 400 degrees Fahrenheit for about 25 minutes.