It's not necessary to clean or polish jewellery When putting it into storage, after prolonged storage, it will need cleaning anyway. Don't use ordinary newspaper to wrap it in, nor use elastic bands to bind several pieces together. After a while the rubber will bond to the jewellery as the band deteriorates and rots, leaving a stain, as will newspaper. Instead, use acid-free paper to wrap items and store where it's not damp.
The Care and Cleaning of your Jewellery
Perhaps the most important thing to bear in mind here is the potential for loss. Always use a bowl of water to clean your jewellery, not the sink. If you stand the bowl in the sink, put the plug in first, and don't remove it again until you're sure you've got all the pieces you started with. It might sound obvious, but you wouldn't believe how much jewellery goes down the drain!
Firstly, check the stone is secure in its claw mounting. Hold the item in one hand and use a fingernail to just touch it. If it's loose you'll see it rock or move. This will need to be repaired by your jeweller first, who will tighten the claws. An old soft toothbrush and warm soapy water is ideal to remove the grease, dust, grit and dead skin that fills the gaps and indentations around the stone anchors of a ring or other items of jewellery. This works equally well for almost all types of stones.
A gentle brush, even an artists brush is infinitely preferable to using a cloth from which threads can be snagged and pulled. If a thread gets caught in a claw, it can bend or weaken the grip of the claw and stones can be lost weeks or months later.
Once again check the stone for movement, just to make sure it wasn't the dirt holding it in place. It should now be gleaming again with a nice new sparkle!
BE AWARE! That some stones are quite 'soft' and others are particularly absorbent. Care must be exercised when cleaning not to scratch them or leave them soaking. They are also best stored in separate compartments of a jewellery box.
General Safeguards
Whilst your jewellery is not being worn, it is best stored in a lined box or soft pouch. Necklaces shouldn't be allowed to become tangled and metal or diamonds can easily scratch other metals or plate, just by being next to each other.
This can ruin or dull a polished surface very quickly, with the obvious disappointment and loss in value that will be the result.
I also would advise against wearing your jewellery whilst gardening, doing housework, or playing any kind of sport, in particular swimming. Jewellery is particularly susceptible to damage from the effects of chemicals present in perfume, hairspray, nail polish remover and deodorant.