Heat a large heavy pan over high heat. Once the pan is hot, reduce the heat to a medium hot temperature and add enough vegetable oil to coat the bottom of the pan thoroughly. Add the fillets to the pan, being sure to leave space between the fillets. Work in batches if necessary. Depending on the specific fish and the pan size, you may be able to cook anywhere from one to four fillets at once. The fillets should sizzle the moment they touch the pan; if they don't, remove them and wait for the pan to get hotter.