Scrub the rusted areas with steel wool or a stiff brush
Wash the skillet with hot water and a small amount of dish soap
Rinse thoroughly and dry completely
If rust remains, scrub with a paste of baking soda and water
For heavy rust, soak briefly in white vinegar and water, then scrub
Rinse immediately after any vinegar soak
Dry the skillet on the stove over low heat
Apply a thin layer of cooking oil all over the skillet
Bake the skillet upside down in the oven at high heat to re-season it
Repeat seasoning if needed to restore the surface