Coins such as quarters can be cleaned using dishwashing soap and distilled water. However, About Coins warns that old coins should never be cleaned. Oxidation should never be removed from a coin; doing so can badly damage the coin's value. The primary reason to clean coins is to help a child start a coin collection using circulating coins, which are typically dirty.
It's important to thoroughly wash hands before cleaning coins. A small plastic container should be filled with warm water and a small amount of dishwashing detergent. A second plastic container should be kept on-hand and filled with distilled water for rinsing.
The quarter should be washed in the first plastic container by immersing it, rubbing both sides gently between the finger and rubbing any dirt off the edge of the coin. The coin should first be rinsed under running tap water while the soap residue is gently rubbed away.
The quarter should then be swished around in the distilled water in order to remove the contaminants found in tap water. At this point, the quarter should only be held by the edges. The coin should be left to dry on a soft cotton cloth. The quarter shouldn't be put away until it is completely dry; this prevents oxidation.