I learned this technique from Kenji López, and it's so good I had to write it down. I've only used it for salmon, but in theory, it works for any skin-on fish fillets.
Kenji uses a thermometer; I don't.
Skin-on fish fillets (1 per serving, about 6 ounces each)
Salt and freshly ground black pepper
2 tablespoons vegetable oil
Dry the fillets with paper towels thoroughly. Season them on both sides with salt and pepper.
In a large skillet, heat the oil on medium-high heat until shimmering.
Place the fillets, skin-side down, on the skillet and immediately reduce the heat to medium-low. Press the fillets gently with a metal spatula to ensure good contact between the skin and the skillet for the first minute (yes, just 1 minute).
Let the fish cook for about 5 minutes. Then, if the fillets resist when trying to lift them with the spatula, continue cooking them until they lift easily.
Flip the fish and cook skin-side up for about 1 more minute.
Transfer the fish to a paper-towel-lined plate and serve!