Scale the fish by placing it in the sink under cold running water. Grasp the fish firmly by the gills and scrape off scales with a fish scaler or small, dull knife. Using short strokes, work from the tail to the head.
To remove the head, first cut through the flesh on both sides with a sharp knife. Then, if the fish is small, slice directly through the spine. For a larger fish, place the knife between vertebrae and tap the back of the knife with a hammer.
To fillet, use a sharp, thin knife. With the bluefish lying on its side, insert the knife behind the gills, and cut in an arc down to just above the backbone. Continue cutting parallel to the backbone toward the tail. Bring the knife up at the tail and remove the fillet. To skin the fillet, place it on a board, skin side down. Run a thin, sharp knife along the fillet between the flesh and the skin.
The secret to successful bluefish cookery is to not overcook. Whichever of the following cooking methods you choose, your bluefish will be cooked when its flesh becomes opaque but is still moist and can easily be pierced with a fork.
To improve the texture of bluefish, marinate the fish in a mixture of kosher salt, herbs, and water. Bring the salt, water, and herbs to a boil, simmer five minutes, then let cool. Add ice, pour brining mixture over the fish in a glass or stainless steel container, and refrigerate for one hour. Drain and pat dry before cooking.
Rinse fish and pat dry with a paper towel. Place whole or filleted bluefish in baking pan and cover with sauce made of liquid, herbs and spices, and vegetables. Bake in the oven at 400°F (200°C) until a knife slice in the thickest part reveals the flesh to be opaque but still moist.
Place whole small fish or fillets directly on greased grill, 4 to 6 inches (10 to 15cm) above prepared coals or fire. Baste with butter, oil, or marinade, and close hood of grill. Cook until opaque and moist on the inside, 6 to 8 minutes for fish less than one inch (2.5cm) thick; 10 to 15 minutes for fish larger than one inch (2.5cm) thick.
Rinse bluefish fillets and pat dry with a paper towel. Place fish on a rack above a baking dish. Preheat broiler and adjust oven rack so fish is 3 to 4 inches (7.6 to 10cm) from the element. Broil, turning once, until fish is opaque but still moist in the center, 3 to 10 minutes, depending on the size of the fish.
Rinse bluefish and pat dry with a paper towel. Dredge in flour and seasonings if desired. Shake off excess flour. Heat frying pan until hot. Add butter or oil. Place fillets in the pan and cook, turning once, until opaque but still moist in the center, 2 to 10 minutes, depending on the size of the fish.