For extra crispiness, let the salmon sit skin-side up on a plate for about 5 minutes.
Rub both sides lightly with the oil. Sprinkle with salt and black pepper on both sides. Do this just before cooking.
Preheat a large nonstick skillet on medium-high heat, then pour in enough oil to cover the bottom (approximately 1-2 teaspoons).
When the oil shimmers (but is not smoking), place the salmon fillets in the pan skin-side down. Gently press each fillet with a spatula for 10 seconds to ensure the skin remains flat against the pan.
Cook for approximately 6-7 minutes until the salmon is around 75% cooked and the skin is crispy. Flip the fillets and cook for another 90 seconds.
Remove from the heat and serve immediately, skin-side up, with lemon wedges.