The basic rule of jewelry care is to apply all lotions, make-up, hair spray, etc. first, then put on the jewelry. Pearls are especially sensitive to the solvents in hair sprays. In the reality of the jewelry business, I see people who refuse to remove rings and those who do so only once in a while. When we clean a customer's jewelry and inspect for wear and loose or missing stones, the jewelry most often needing repair is a ring that is "never" taken off the finger and cleaned by the owner.
Persistent dirt gets between the metal settings and the stones causing abrasive wear and sometimes sometimes a loose stone. Everyday wear on the outside of stone settings may lead to lost stones, too. A regular home cleaning and good look at the jewelry will prevent most stone loses, allowing for repair or tightening before it is too late. It is not common to see really clean jewelry come into the shop. When we do, that jewelry is generally in much better condition than the dirty items.
Hand lotions and soap film are some of the more difficult materials to remove. With CZ stones, a clean stone is vital to keep the "sparkling diamond" look. Just a little lotion on the bottom of the stone will take away much of the visual life of the stone. Fortunately, CZ's are fairly hard and tough. Cleaning may be more aggressive than with stones like opal or pearls, for example.
Start by taking the ring off the finger long enough to clean it! Using a soft tooth brush and a warm to hot solution of a dishwashing detergent like Joy, brush as well as possible to remove the scum and lotion. Rinse well in warm water. Pat dry and take a look. If more cleaning is needed, soak the ring in hot tap water with about 1/3 detergent to 2/3 hot water. (The mix is not critical.) Then brush again.
The brush and even the end of a toothpick will not damage the stone. Do not use any abrasive cleansers. Most will not damage a CZ but will take the shine off the metal and may scratch some softer kinds of gemstones. Do not use toothpaste or similar stuff. Short of buying a small home sized ultrasonic cleaner, the detergent approach is one of the best for home use.
With CZ a little sudsy ammonia may be added and will greatly improve the cleaning speed and effectiveness. Do not use any ammonia cleaners with silver, turquoise or pearls. Ammonia will cause spots on sterling. Use enough ammonia to liven up the fault hearted and do have a window open and some air moving.
With regular cleaning, you "get to know" the jewelry and can spot worn metal and loose stones before a loss happens.
When you can not get the dirt off, let the jewelry store clean and inspect the jewelry. Strong detergents in heated ultrasonic cleaners followed with high pressure steam cleaning will remove most all dirt. Soap scum takes a little longer but comes off ok.
CZ is hard enough to cut glass. Most faceted gemstones are hard enough to cut glass. However, dust in the air contains a lot of silica (think sand). Hand lotions will leave a film on jewelry for dust to stick to. Over time, this rock dust in the air will abrade metal settings and some softer gemstones. Keep the lotion off the jewelry if at all possible. Not only does lotion free jewelry sparkle and look better every day, it will wear longer, too.