In a mixing bowl, combine the extra virgin olive oil, fresh dill, fresh oregano, black pepper, and salt. Squeeze in the juice of half the lemon and mix well until all ingredients are thoroughly combined.
Place the salmon fillets in the bowl with the marinade, coating each piece generously. Let them marinate for at least 15 minutes; if you have more time, letting them sit for up to an hour will deepen the flavors.
If you’re using a skillet, heat it over medium-high heat. For grilling, preheat your grill to medium heat. A well-heated surface ensures a nice sear on the salmon.
Once the skillet or grill is hot, place the salmon fillets skin-side down (if using skin-on) on the cooking surface. Cook for about 4-5 minutes on each side, depending on the thickness of the fillets. The salmon should be opaque and flake easily with a fork.
Once cooked, remove the salmon from the heat. Squeeze the remaining half of the lemon over the fillets for an extra burst of flavor. Serve warm on a platter, garnished with additional fresh dill if desired.