Try using an old tooth brush with some toothpaste. Add a couple drops of water. Shine away. It is a quick way to bring back the shine. Afterwards you can buy a polishing cloth at most department stores jewelery counters.
The tips, hints and ideas at TipKing are vetted prior to publishing however some methods remain speculative in their own nature; therefore the information should be used responsibly and at your own discretion. The Information is displayed on an "As Is" basis, without warranty. Full disclaimer