The most well-known fact is that an emerald will always show visible inclusions. That's it.
In fact any emerald without inclusions is suspected to be synthetic or imitation. Affectionately, and rather poetically, the specialists call the numerous crystal inclusions (which are caused by calcite deposits) and fissures,  "jardin". They regard the tender little green plants in the emerald garden as features of the identity of a gem which has grown naturally.
 
In an emerald, color is paramount. Its green is incomparable! And as the ancient Roman historian  "Pliny the old" said  "no green soothes to the eye as the green of emeralds". The finest have a deep, intense, glowing green, and associated with a good, crystal clarity and a decent carat weight (let's say anything over 2 carats), will command huge prices. In its finest grade, an emerald is more valuable than a diamond of equal carat weight.
However, medium colors with good clarity can be beautiful, and...affordable if found in the right place. Beware that many jewelers and dealers out there will sell any quality for artificially high prices! 
Colombian emeralds are the most valuable in the market place, but this is not the rule. The main Colombian mines are are Muzo, Coscuez , Chivor, La Pita, Gachala', Plena Blanca, Totumos, Polveros, Cunas.    As a generald rule, Muzo and Chivor emeralds are green with bluish overtones, while from Coscuez have yellowish overtones. 
In the past decade or so, also Zambian emeralds have gained so much popularity to overshadow the fame of Colombians. They usually are very clean, with medium to fine green with bluish-graysh cast.

Faceted emeralds come in a variety of shapes: rounds, pears, ovals, emerald-cuts, cushions, cabochones. But it is the "emerald cut" or octagon that is the most popular and classical shape for emeralds. The reason why this shape is so "popular" has to do with the natural shape of the rough crystal and its cleavage. Following in order of popularity or better of availability, pear shapes, ovals, marquises, rounds. Round shapes over 1/2 carat in weight are very rare and always command premiums.
Cabochon cuts are the oldest way to cut emeralds before the world knew faceting methods. As in facet grade material, also cabochon emeralds come in different grades. Do not think that cabochon emeralds are low grade gems. We saw a parcel of gorgeous deep, glowing green, clean cabochons of Muzo origin that were selling wholesale for $3,000 per carat.
All emeralds are oil-treated when they are cut to reduce the likelihood of fracture. This treatment is perfectly acceptable in the gem trade. However, coloring emeralds with green substances is unacceptable, unless disclosed.