It feels great to clean coins with stuff from around the house as it's sort of 'free' but often it really doesn't do the job, especially when the coin may be fragile, rare, etc.
The choice of best cleaning agents depend on what environment the coin has come from and what the over-lying layer is composed of. I can only speak from experience of coins from standard soil found in the UK which varies from sandy / peat / clay based. A specialist cleaning material based upon a 10% Sodium Hexametaphosphate / 90% good old water is excellent for soaking and will dissolve / loosen most deposits in a matter of minutes. Clean bronze / silver objects separately and take the coin / artifact out regularly to inspect removal of deposit and aid with soft bristle brush (old toothbrush). Once most of the calcium based deposits have come off I like to let the item dry. Bronze can then be brushed lightly with bristle brush and either dipped in molten micro crystalline wax or given light wipe with olive oil / petroleum jelly. This seals the surface to stop oxidation that is found (esp. 'bronze disease' on bronze / copper coins) and enhances the surface patina color. If the surface details are very slight on any type of coin (usually lowers value so no harm..) I rub with abrasive pencil eraser to lighten raised details to stand out from darker background. Silver coins can have final cleaning with neat trick (esp. good on medieval hammered coins from Europe)- take aluminum cooking foil, lay coin on flat piece of foil, spit (I kid you not!!) on coin and fold foil over to cover coin. Hold coin gently between finger and thumb and wait until heat generates (chemical reaction with surface deposits) you may also notice smell of rotten eggs. Do not leave too long or coin may be damaged - a little at a time is always best when cleaning. GENTLY wash and rub coin between finger and thumb and any legend details should stand out bright and shiny against a slighter darker background. I sometimes enhance the toning by application of very small amount of black shoe polish / wax then rub off again.

Sorry so long but hope that may be useful.
 
 
 

From Andy Sabich:

We used these methods on several coins we found with great results.

I picked up an interesting trick from a fellow treasure hunter in Spain when my family and did some detecting there last summer on Roman sites. He works for the University and knows many of the archeologists there and what they do is one of the following:

1. Soak the coins in distilled water and then put them in the freezer. The water will have gotten into the dirt and the ice crystals expand and break the dirt apart. Several repetitions will be needed to completely remove the dirt; however, it does not damage the coin.

2. Spread a layer of Elmers white glue over the coin with the coin laying on a piece of wax paper. Let the glue dry and then pull it off the coin. Again, a layer of dirt will be pulled from the coin without damaging it. It will require several tries to clean it completely.
 

The Mayors Cleaning Method

For getting black tarnish off silver and also works well on nickels.
You need to go to the grocery store and pick up a box of Arm & Hammer washing soda
(not baking soda) available in the laundry detergent dept. Take a sheet of aluminum foil and fold it
into a strip about 2 inches wide. Place it in the bottom of a glass container and place the coins on top of it. Put a couple tablespoons of the washing soda over it and pour in boiling water till its covered with about an inch of water. When it stops fizzing take the coins out and rinse with water, or to shine them up nicely rub with a paste of baking soda and water.