The best care is preventive care. When you remove jewelry, rub it gently with a soft cloth or hand towel to remove body oils and salts from the jewelry's surface. Store individual pieces in the small plastic bags provided. This will not only prevent tarnish, but will also prevent surface scratches.
You may use commercial dip solutions on plain metal items only. Never, never put anything with a pearl or a semi-precious stone in a dip. Paste polishes are fine and can be rinsed off with very warm water.
For a quick and easy treatment, take a pinch of baking soda between your fingers and rub over the metal surface, rinse with warm water and dry well. Baking soda is a very fine abrasive that will remove some light tarnish.
For necklace chains that have been worn on a hot summer day, lather your hands with a mild soap (put the stopper down on the sink drain first!), coil the chain between your palms and gently rub your hands in a circular motion. Rinse well and dry throughly, even using a hair dryer on the low setting to dry tightly linked chains.