Harvey, there are many helpful tips in the Cleaning and Storage of Finds section of the forum.
Unfortunately, some coins are just corroded or pitted too severely to be helped much. In these cases, excessive cleaning will just make them worse and will result in loss of detail.
For my copper and nickel coins I use a wet wash cloth with some Dawn dishwashing liquid on it. I just rub the coins with the wet cloth and then rinse them off. If it is a nicer copper coin I will give it a coat of olive oil to preserve it. Some people also use renaissance wax for this.
On my silver coins, I never rub them because that will scratch them. I just hold them under the running water until most of the dirt is washed off. If there is any stubborn dirt remaining, I will dab them with the wet, soapy wash gloth, then rinse them off. For 99% of silver coins this will get them nice and clean.