Hockeyplayer--
I don't generally clean my jewelry finds unless they are really crusty, but silver and gold rarely get that way. In fact ring # 2 (above) had some pasty white stuff on it. I sprayed it w/ a little organic orange cleaner (similar to turpentine, but very weakly diluted) and went over it with a toothbrush. Usually soap and water are all you need. For diamonds, you can use toothpaste and a toothbrush to get the scum off.
Silver can be cleaned w/ a short dip in white vinegar (5% from any grocery store) w/ some aluminum foil. Take it out and put it directly in baking soda (without drying it) and scrub it with a toothbrush, but I don't recommend this for coins unless you don't care about losing value. And if your piece is plated, the plating will come off.
Turpentine works because it will dissolve any grease/ oil, without affecting the metals. Don't use window cleaner unless you check first to be sure it doesn't have ammonia, or you can cause pitting in your finds-- it does dissolve precious metals.
Hope this helps!