Sautéing is probably the easiest way to cook thin fish fillets. As you cook them in a small amount of hot fat on top of the stove, it's important to sauté the fish in a pan that's heavy enough to distribute the heat evenly. A professional sauté pan (available at any restaurant supply store) or iron skillet is ideal.
When you sauté fish, use enough oil (or butter and oil) so that the surface of the pan is generously coated. Make sure the fat is hot before you add the coated fish or it'll stick to the pan. Place the fish in the hot oil, leaving ample space between the fillets, and cook the fish uncovered. Otherwise, the fish will steam rather than fry, and the coating will be soggy rather than crisp. Sauté the fillets until they are a light golden color on each side, turning once. Serve immediately.
From the "Legal Sea Foods Cookbook" by Roger Berkowitz and Jane Doerfer, illustrated by Edward Koren.