The simplest way to keep your gemstone jewelry beautiful is to mix mild liquid detergent (hand soap works) with warm water and use a soft bristle toothbrush to gently scrub away the dirt and film. (Remember to clean the underside of the jewelry too!)
If possible, remove your jewelry when doing physically-intensive work, like working out, or cleaning with harsh household chemicals.
You should keep your jewelry in a jewelry box that has a tough exterior and soft interior (ahem, your ITR box works!). A jewelry box with compartments will also come in handy because you will want to separate your jewelry into separate categories (silver, gold, diamond, pearl) to prevent them from damaging each other.
Also remember to store your jewelry away from excessive heat or direct sunlight because this can cause long term damage. Excessive heat can cause certain metals to change colors or even cause certain stones to lose its deep colors.
A carat represents the weight of a stone. It is evaluated on a point system where one carat (1.00) is equivalent to 100 points.
A karat represents a standard measurement for gold. A karat is divided into 24 parts where pure gold is 24 karats which means that 24 out of 24 parts are gold.