Gold Coins
Fill a bucket with warm water and soap. If possible, the water should be distilled. Take a soft toothbrush or cotton washcloth and dip it in the bucket, then gently rub it over the coin until the coin is clean. Because gold is soft, it scratches very easily. Gold coins are the most unlikely coins to discolor during cleaning, though.
Silver Coins
Fill a cup with ammonia, vinegar, rubbing alcohol or lemon juice. Place the silver coins in the cup and allow the coins to soak until the dirt has lifted off of the coins. Air dry the coins. Note that among collectors, cleaned silver coins are not desirable. Many collectors simply will not purchase coins that look like they have been cleaned. So even if your silver coins have taken on a dark tone over time, you might consider leaving them uncleaned, provided you can still see the text and design on the coin.
Copper Coins
Fill a cup with olive or grape oil and soak the coins in the oil. Then, air dry. Copper coins are more susceptible to damage through cleaning than gold and silver coins. Thus, if you have dirty copper coins, you might want to consider purchasing a specialized commercial cleaning product or taking your coins to a professional coin cleaner.