While this is cooking, grab another frying pan and heat the vegetable oil at medium-high heat. Once the oil is hot, place the Salmon on the pan skin-side down. Make sure the oil is hot, in order to keep the skin of the salmon from sticking to the bottom of the frying pan. Gently press down on the fish to help it keep its shape, since it tends to curl up during the first minute. Keep cooking for about 3 minutes in total.