Scrub the rusted area with steel wool, a scouring pad, or a stiff brush
Use warm water and a small amount of dish soap if needed
For heavy rust, soak the pan in a 50/50 mix of white vinegar and water for a short time
Check frequently while soaking to avoid damaging the cast iron
Scrub again after soaking to remove loosened rust
Rinse thoroughly with warm water
Dry completely with a towel
Heat the pan on the stove or in the oven to remove all moisture
Apply a thin layer of cooking oil to the entire surface
Bake the pan upside down in the oven to re-season it
Repeat seasoning if the surface still looks dull or dry