Color
Color can be slightly misleading, because many crystals come in a variety of hues. However, depth of color is always important. Look into the center of the crystal. If you see a pale, transparent spot, there's a chance you're holding a piece of glass.
Hardness
It's worth acquainting yourself with Moh's scale of hardness, which says that diamond can scratch corundum (ruby and sapphire,) which can scratch topaz, which can scratch quartz, which can scratch feldspar (moonstone.) Obviously you can't grab a piece of jewelery off a stall and take a nail-file to it, but do check the crystal for blemishes under a jeweler's loupe. Emeralds, for instance, are comparatively soft and it is not unusual for individual gems to sustain scuffs.
Context
Crystals serve different purposes depending on their toughness, rarity and size. For instance, the small red stones known as garnets have always been too plentiful to be precious. Their softness means they are less suitable for hard-wearing jewelery such as rings and bracelets, but in the Victorian era they were imaginatively employed in brooches and long necklaces. A large reddish or yellowish brown stone mounted in a silver brooch will almost certainly be a Caingorm or Scotch topaz--in fact, not topaz at all, but a variety of smoky quartz.
Cut
Crystals are cut to enhance their natural properties. The three chief cuts are brilliant, step and cabochon. A brilliant cut has a flat crown, a generally circular shape and 58 facets. This is used for diamonds. A step cut, used in particular for emeralds and topaz, is eight-sided with a more rectilinear appearance. In cabochon cutting, the stone is honed into a smooth, rounded shape, without facets. Opals, moonstones, cat's-eyes and larger garnets are usually presented "en cabochon."