Fill two clear bowls with liquid; one bowl with white vinegar and the other bowl with cola soda. These two liquids are highly acidic and will be able to take the oxidization off the pennies.
Place one oxidized penny into each bowl, and allow the pennies to sit in the liquids for at least 20 minutes. You will see the coating on the pennies start to disappear.
Fill a third bowl with water and add in 1 teaspoon of dish soap. Mix well, and place the pennies in the soapy water.
Dip a towel in the soapy water, remove the pennies, and scrub off the pennies slightly. The oxidized coating will come off, revealing new-looking shiny pennies. Rinse the pennies in plain water.