For bigger pieces, use baking soda and a clean, damp sponge. Make a paste of baking soda and water. Scoop the paste onto the sponge, and rub the paste into the silver. Rinse with hot water and polish dry with a soft, clean cloth.
For badly tarnished silver, leave the baking soda paste on the silver for an hour or so, before cleaning off with the help of the sponge and hot water.