Scrub it with a steel wool pad and hot water. Never soak the pan for any length of time - just briefly wash it out. Rinse thoroughly, then dry with paper towels. NEVER put cast iron cookware in the dishwasher.
Place the cleaned cast iron frying pan on the heated burner of your stove for a minute or two to make sure that it is bone dry. While the pan is still hot and on the stove burner, lightly oil inside of pan with a neutral cooking oil.
Neutral Oils - Use vegetable oils (canola, sunflower, etc.), shortening (like Crisco shortening) or lard.
Leave frying pan on the hot burner of stove for a few minutes. Remove from hot burner and wipe excess oil off the pan with a paper towel.
Store your cast iron cookware with the lids off (especially in humid weather, because if covered, moisture can build up and cause rust). Be sure that you place a couple paper towels inside your cast-iron pan when storing to make sure that any moisture that forms will be absorbed by the paper towel. Never put the utensil in the dishwasher or store it away without drying it thoroughly.
If your skillet has not been seasoned or is need of reseasoning (food sticks, rust, etc) see How do I season a cast iron skillet.