It is fairly easy to clean coins using common household materials. However, be warned that by cleaning a coin, you could be drastically reducing its value. If you suspect a coin may be valuable, always have it cleaned and evaluated by a professional. However, if you want to clean up a coin for display and not for resale in the future, you can use a homemade coin cleaner.
Olive Oil Method
The most gentle method of coin cleaning involves olive oil. Allow the coins to sit without overlapping in a pool of olive oil. The coins will need to stay submerged for a few days or as long as a few months, depending on the level of corrosion. Change the oil periodically when it appears dirty. Remove the coins and gently roll a cotton swab over the surface to dislodge the grime. This method minimizes scratches on the surface.
Washing Soda Method
Another method you can try involves using Arm & Hammer Super Washing Soda (found in the detergent aisle). Washing soda contains sodium carbonate, whereas baking soda is sodium bicarbonate. Using the washing soda method will work on only brass, copper and silver coins. The method sometimes works on nickel coins but rarely on iron.
Line a shallow bowl with aluminum foil. Combine a few tablespoons of washing soda with near-boiling water into the bowl, and add the coins in a single layer. For the best results, clean each coin with a coin made of a similar material. The mixture will fizz. Wait until the water has cooled to room temperature, and then remove the coin.
For copper pennies minted before 1982, use a blend of 1/4 cup white vinegar and 1 tsp. of salt. Mix these together in a small bowl until the salt is dissolved. Add the pennies, and let them sit for at least five minutes. Then use a toothbrush or a cotton swab to remove the grime, which should be loosened, and then rinse under cold running water.
Because pennies minted after 1982 contain mostly zinc, this method won't work on newer pennies. Instead try loosening the grime with a pencil eraser or by using a diluted vinegar mixture.