Strip rust from a cast iron skillet and re-season it so it is smooth, black, and ready to cook.
Scour the rusty areas with steel wool or a stiff brush and a little dish soap (soap is fine here since you will re-season). For heavy rust, soak in a 50/50 vinegar-water bath for up to 1 hour, then scrub — don't leave it longer or the acid pits the iron.
Rinse off all rust flakes and dry the pan thoroughly with a towel, then set it on the stove over low heat for a few minutes to evaporate every trace of moisture. Any leftover water flash-rusts.
Rub a very thin layer of neutral high-smoke-point oil (grapeseed, canola, or flaxseed) over the entire pan, inside and out, then wipe it back off with a clean cloth until it looks nearly dry. Too much oil turns gummy.
Place the pan upside down in a 450-500°F oven with foil on the rack below to catch drips. Bake 1 hour, turn off the oven, and let it cool inside. Repeat the oil-and-bake step 2-3 times for a durable black finish.