First of all: keep them clean! Rings in particular tend to collect dust and soap behind the stone, particularly if you wear them all the time. To clean transparent crystalline gemstones, simply soak them in water with a touch of gentle soap. If necessary, use a soft toothbrush to scrub behind the stone.
Even the hardest gemstone variety can be vulnerable to breakage if it has inclusions that weaken the crystal structure. Exercise common sense: if you have a ring set with a softer gem variety or an included stone, take it off before strenuous exercise.
Diamonds are very hard but can shatter in two with a single well-placed blow. Rubies and sapphires are the toughest gems but even they can chip if hit sharply.
Think twice before putting gems in an ultrasonic cleaner. Diamonds and rubies and sapphires will be fine but many other gems may not be: when in doubt, leave it out. Diamonds, rubies and sapphires, and other single-crystal gems can be cleaned with a touch of ammonia in water to remove all films and add extra sparkle.
Opaque gemstones like lapis lazuli, turquoise, malachite, require special care. Never use an ultrasonic cleaner and never use ammonia or any chemical solution. These gem materials should just be wiped clean gently with a moist cloth. These gemstones can be porous and may absorb chemicals, even soap, and they may build up inside the stone and discolor it.
The reason why these materials need more care than transparent gemstones is that these materials are essentially rocks, not crystals of a single mineral. Think about it: when you put a rock in water, it absorbs the water and is moist all the way through. A single crystal gem like sapphire will not absorb water: all the molecules are lined up so tightly in the crystal that there is no room for water to enter.
Opals also require special care. Never use an ultrasonic, never use ammonia, and avoid heat and strong light which can dry out the water in opals.
Organic gems like pearls, coral, and amber should only be wiped clean with a moist cloth. Due to their organic nature, these gems are both soft and porous. Be careful about chemicals in hairspray, cosmetics, or perfume: they can, over time, damage pearls in particular.
Store each piece of gemstone jewelry separately so that harder stones don't scratch softer ones. Almost every gemstone is much harder than the metal it is set in. Gems can scratch the finish on your gold, silver or platinum if you throw your jewelry in a heap in a drawer or jewelry box.
