How can you identify a genuine emerald?

A real emerald is usually recognised from its special jardin, meaning internal inclusions, then from a certain refractive index that sits roughly between 1.577 and 1.583, and also from how it reacts with a Chelsea filter, where it often shows up as pink or red, not always, but frequently.

Natural emeralds seldom have perfect clarity; when you look with magnification, the existence of three-phase inclusions, gas plus liquid plus solid, is a strong hint of natural origin. Synthetic emeralds often show flux patterns or hydrothermal growth instead. Also, natural stones tend to show slight dichroism; you can see blue-green and yellow-green tones when you change the viewing angle.