Summary: The 4 C's are Color, Clarity, Cut, and Carat.  The result of inspection is what decides the order of the C word.  There are many ways to cut and set the stone to show off its best features or to camoflauge flaws. 
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We all have probably heard of the Four C's: Color, Clarity, Cut, Carat.  These are used to get the value of a stone.  The beauty of a stone is determined by the same C's but in different order: Cut, Color, Clarity, Carat.

• Color is the body color of the stone.
• Clarity is the degree of flawlessness.
• Cut also includes the proportion of the stone.
• Carat is what the weight of the stone is.

When examining a stone for value or beauty, one must keep in mind its faults.  To do so, the stone must be examined under excellent light from many angles.  Some of the common faults found in stones are as follows:

Type of Flaw	Description
Chipped Culet	(stone bottom point)
Fringed girdle	Small radial cracks penetrating the stone from the girdle
Bearded girdle	Similar, but can be repaired by repolishing, without much loss  in stone weight
Girdle too thick	Too much weight will in girdle, so, for its weight, it will be smaller in diameter than another stone of comparable weight.

Common cut process:

Put pointed end of the diamond (let's say) against a turning wheel that held another diamond, then grind off the point of the diamond, creating a large, flat surface.  This flat-top looks like squarish shape and is called a table top.

Type of Cut	Description
Rose-cut	Its base is flat and its facets, which are in multiples of six, give it a flower-like appearance like an opening rosebud.'
Cushion cut	Oval with squarish corners.  Crown is  higher than the table facet and much smaller in diameter.  Culet was open instead of a point.
Holder cut	Higher crown, small table-facet, and an open culet.  Round in shape, crown not as high nor table as small

Common settings:

Type of Setting	Description
Bezel	Rim holds the stone and completely surrounds gem.  Bezels have straight edges, scalloped edges, or can be molded into any shape to accommodate the stone.  The backs can be open or closed.  Can make stone look larger or can even conceal nicks or chips.
Collet	Like bezel, but uses gold tubing (very rare and done by highly skilled masters)
Prong	4 or 6.  Can be pointed, rounded, flat or V shaped.
Gypsy	Metal at top of ring (around stone) is much heavier than shank.  The stone is set flush into hole at top.
Flat-top	Faceted stone is placed into a hole in the flat top of the metal and then held in place by small chips of metal attached to stone's girdle.  Sometimes metal chips areworked in beads.
Channel	Into channel with no metal separating them.
Bar	Like channel.  Circular band.  Stones held by long thin bar instead of prongs shared between two stones.
Pave	Numerous small stones.  Like paved with stones.
Cluster	One large stone and several small accent stones.