This is the simplest way to cook a fish steak, I like Jewfish, but you can use what ever you have. Sometimes I add extra flavours to the flour like garlic powder or that powdered parmasean cheese stuff.
Mix together the flour, salt and pepper in a shallow bowl or on a plate.
Lay the fish into the flour then turn so a dusting covers the whole fish fillet.
Turn on a frypan to a medium heat, you need to have it so it browns the outside but also cooks the middle. Thus a little lower for thick steaks and little higher for thin steaks.
Place the butter and oil in the frypan, when melted add the fish and cook until brown, then turn. If the outside is brown but it still isn't cooked all the way through you can put it in the oven to finish it off without needing to be worried about burning it.