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The Baking Soda Method
Mix 1/4 cup each of baking soda, liquid dish soap and salt into 1 gallon of water in a large aluminum or iron pan. Place the coins into the solution and heat it to boiling. Take the pan off the heat and allow it to set for about five minutes. Drain the solution from the coins and gently wipe each one dry with a microfiber cloth or a small brush. The solution should become very cloudy and murky as the silver sets. If you do not have an aluminum or iron pan, then add some balls of aluminum foil or iron nails to the solution.
Alternative to the Baking Soda Method
Soaking the coins in vinegar or lemon juice may also be effective. Place the coins in a container and pour the vinegar or lemon juice over them, covering them completely. Do not boil the mixture, but allow the coins to set, completely submerged, for a few hours. You may also add iron nails or balls of aluminum if you are using a non-metal container, in which case you should allow the coins to set for no longer than 30 minutes. Drain the solution from the coins and clean as directed above.
Other Advice
Do not leave the coins in any solution for more than 12 hours. If the coins are kept submerged for any longer, the solution could damage the surface of the coins and reduce their value. Check on the coins periodically during soaking to ensure that no surface damage has occurred. If the coins are very old or rare, it may be best to have them cleaned by a professional.