Loosen Dirt and Particulates
Dirt and particulate buildup is normal for any coin collection and appears as a dark brown or black film on a coin's surface. Gently loosen this film with an old toothbrush or fingernail brush dipped in warm water. Even if the film is thick, it is best to rub the coin gently with your brush and wait for the dirt to loosen. If you scrub too aggressively with the brush, you may accidentally rub away some of the coin's features and finish.
Soak
Once you have removed any surface stains, you will need to soak the coin if you see any rust or chemical buildup. Chemical buildup will most often show up as green or red discolorations that pool together as a thick solid or as a thin membrane. If the discoloration is a thin membrane, dilute 1/2 cup vinegar with 1/2 cup water and let the coin soak in the solution for a few minutes, then remove it and set it on a towel to dry. If the chemical discoloration is a large solid clump, soak the coin in a one-fifth solution of CLR.
Rub Away Solids
After you have soaked the coin, rub away any remaining solids with a soft cloth. You can also use this cloth to roughly polish the coin once you have finished cleaning it. Note: Do not use metal polish on your coins, as these solutions often contain harsh chemicals that can corrode your coins over time.
Tarnish
If you have silver coins that experience natural oxidation, most commonly referred to as "tarnish," it is important to leave this alone. Because the chemical properties of the coin have changed, this natural discoloration cannot be cleaned or removed; attempting to do so can damage your coin. Additionally, an age-appropriate amount of tarnish on a coin can actually add value to it.