Preparing
Purchase a box of Arm and Hammer Super Washing Soda. This is different from the typical baking soda. This will be the main ingredient when cleaning your coins.
Get a large glass bowl or dish and cover it with aluminum foil. Make sure the foil is flat and does not have any large creases in it, which may result in having dirty spots when the coins rest on the foil during the cleaning.
Cleaning
Boil a pot of water. The hotter the water, the better. Once the water begins to boil, pour it into the glass bowl covered in tin foil. Drop in coins that you want to clean. If you plan on doing more than one at a time, make sure they do not touch. In addition, it is probably best if you do not mix metals while cleaning (so do not wash pennies and quarters at the same time). Once the coins settle, pour in 2 tsp. (more if the corrosion is heavy) of the Super Washing Soda into the hot water and stir until the powder is partially dissolved.
Process
Allow the water to sit and cool to room temperature. As this occurs, you will see the buildup on the coins begin to dilute the color of the water. Once the water is at room temperature, remove the coins from their bath. They should be completely clean now. However, if they are not, repeat the process by pouring the water out and placing new aluminum foil onto the bottom of the glass bowl. Boil more water and repeat the process. Multiple washings will not damage the coins at all.