For general silverware, the technique is pretty basic and simple. You need to take a heat proof glass dish. If that is not available, a thick plastic dish will also work well. Place a large piece of aluminum foil on the base of the dish. The shiny side of the foil needs to be on the top. Add a table spoon of baking soda and salt on to the dish. Now add one gallon of boiling water and make sure that you stir well so that all the constituents of the solution nicely gel together. Add the silverware to the solution, ensuring that it is fully submerged and touching the surface with the foil on it. The tarnish will go away after sometime. Rinse it with warm water to remove any residue. Remember that this is not an ideal technique for more delicate silverware such as jewellery.
When dealing with silver jewellery, greater caution needs to be exercised as it is delicate and can be easily damaged. Make a thick paste of the baking soda with water. Apply it to the jewellery and rub it gently. Once the tarnish is removed, rinse it with warm water and clean it with a soft cotton cloth to give it a nice shine.
Toothpaste can work well on light silverware. You need to put the toothpaste on the surface of the silverware in a manner that it forms a light layer on top. Use a few drops of water to form some lather and foam. In case the tarnish is tough, you can use a soft toothbrush to clean the silverware. Rinse with water once cleaned and dry it with a soft cloth.