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Hardness
All gemstones have a certain hardness, which is essentially the strength of the bonds of the molecules making up the gemstone. There are many ways to test for hardness, but the Mohs hardness scale, though somewhat arbitrary, is suitable for an amateur and requires only a material to scratch the gem against. The Mohs scale goes from a hardness of 1 to a hardness of 10, with 10 being the hardest, a diamond. If you scratch a gem against a piece of glass, for instance, and it scratches the glass, then the gem has a hardness greater than 5.5, the hardness level of the glass. This can help you get an idea of how hard the gem is, and thus help identify the gem.
Habit
Gems have habits. The word habit, in this context, refers to the shape of the crystal. When crystals form, their molecules create very specific structures. Gems tend to form certain structures; for instance, a diamond will usually form an octahedron, but can also form into a macle, dodecahedron or cubic shape. Identifying the crystal structure of a rough stone can, in turn, identify which type of gem it is.
Color and Luster
While not conclusive, color and luster are nevertheless important aspects to note when identifying a gem. Some gems will only come in one or two colors, while others come in many colors; for instance, while sapphires are generally thought of as blue, they can actually be yellow, pink and green as well. Rubies are essentially red sapphires. Sometimes an unusual color can make a gem have more or less value. Luster refers to the shine of a gem, how light reflects off of its surface. Luster can be pearly, metallic, waxy, dull, and so on. Learning what luster type a gem has can help identify it.
Specific Gravity
The specific gravity of a stone refers to the ratio between the weight of the stone when compared to the weight of an equal volume of water. Determining specific gravity can be a little complex, but is very helpful in determining the identity of a gem. Holding a gem and feeling its heft, or whether it seems heavy or light in comparison to its size, is a very crude way of determining specific gravity but makes for a very fast assessment. You can more accurately determine specific gravity by using a kit with heavy liquids and observing whether a stone floats or sinks in liquids of different densities. You can also use scales and suspend a stone in a beaker of water. While time-consuming, the water method is very safe and accurate.