Before we worry about "how" to facet let's tackle "what" to facet.
	In general the purpose of a facing a stone is to create something more beautiful with it than mother nature did. It will then be placed in some kind of display device (jewellery) and be used to adorn an individual. From this set of requirements we can discern or intuit several desirable features for a faceted gemstone.
	Durability	The stone must be strong enough to survive both its mounting and the rigors of the world. Ring stones and cuff links must by necessity be able to stand daily contact with the world, have resistance to abrasion, chemical resistance, and the ability to survive a few incidental "knocks" with breaking. Necklaces and ear rings can be somewhat less durable as are necks and ears.
		Hardness	The ability to withstand scratching. Quartz or silica has a hardness of 7 and is the most abundant material present in "dust", hence a harness of 7 or higher is desirable in rings/cuff links. (diamond is the hardest)
		Cleavage	The ease at which a stone when struck a glancing blow will naturally split into one or more additional pieces. Strong cleavage is NOT a desirable trait of a gemstone.
		Toughness	Tough stones can withstand pressure and force, but not necessarily scratching. A tough stone can withstand a blow without breaking, cleaving, or splintering. (Jade is the toughest of all gemstones.)
	Color	A stone must display some kind of color to be desirable. In a sense transparency is also a part of color. Gemstones must be very transparent and return to the viewer some kind of color or sparkle. It is possible for gems to be "too light" and equally possible for them to be "too dark". so there is a "correct and desirable" level of color for gemstones.
		Chemical Impurity	Most colors in the gemstone world are caused by one of two factors, and a trace element or impurity is one. Both Ruby and Emerald claim their colors from a small amount of chromium in the crystal structure.
		Physical Structure	Some colors in the gemstone world may be due to crystal lattice defects, or inclusions. The catseye effect is usually caused by smaller parallel crystal growth within the main body of the gem. Smokey quartz gets its color form radiation damage of the crystal structure.
	Optical Properties	The index of refraction of a stone is important as well as its dispersion. Clarity might also be an optical property as well as visible flaws, imperfections in the crystal structure.
		Index of Refraction	When light travels from medium to a second, it is "bent" and the degree to which it is bent is called refraction. More dense gemstones tend to have higher R.I. values.
		Birefringence	Multiple R.I. values defined by crystal direction. Not found in cubic minerals. Will increase the effective number of facets.
		Dispersion	Since "white light" is made up of the entire color spectrum, dispersion is the property of bending one color more than another. Dispersion beaks the white light into multiple colors forming rainbow type effects. In most colored stones this is not important. diamond and zircon have high dispersion.
	Rarity	This is NOT necessarily a desirable property, it does affect the value of a gemstone. Some stones like diamond have strongly controlled availability and may not have true rarity. Other stones may be so rare as to have little value because they are not seen enough in the market place to generate market interest. From the point of view of the gem cutter, this is not an important trait. From the point of view of the gem seller it certainly is. Sometimes they are one and the same person! Go figure.