For best results, use a soft cleaning cloth that is lint free. Glass polishing cloths are very effective, as is chamois leather or synthetic chamois. Fluffy cloths or towels, are no nos, as the threads may catch in claws, and spoil the appearance, as well as weakening the setting. If you own a pair of glasses or sunglasses it is likely to have come with the right polishing cloth for your jewellery.
Either use a mild solution of soap and warm to hot water, or buy a jewellery cleaning solution. Make sure you immerse your jewellery fully in the solution. An old toothbrush is very effective. Make sure you scrub in all the crevices, and remove all soap afterwards. Rinse with hot water and your stones will sparkle.
A more intensive clean for polished jewellery is to dab cleaning liquid generously onto the jewellery. Polish in a gentle, circular motion, making sure to cover the entire surface of the metal. Next, using a dry area of the cloth, polish the newly cleaned metal, again using a circular motion. This will remove any excess cleaning fluid, and give your jewellery a deep, clear shine.
Ultrasonic cleaners are good for cleaning diamonds and precious stones (although opals and tourmalines do not get along with them). But for most, hot water and washing liquid is amazingly effective. If cleaning your jewellery over a sink, make sure you do it over a sieve as the last thing you want is for your precious pieces to vanish down the plughole!