Types of Salts
The salt we are most familiar with is common table salt, sodium chloride (NaCl). In chemistry, there is acidic, or hydrogen salt, such as calcium phosphate, which is used in baking soda. Basic, or alkali salts such as potassium cyanide are formed by hydrolysis. Any type of salt can form a crystal, because the catalyst is a saturated solution that is evaporated in some way.
Seed Crystals
To grow a crystalline formation in the case of salts, a seed crystal must be submerged in a supersaturated salt solution. A seed crystal is a small crystal that is treated in some way to encourage further crystallization.
Crystal Gardens
To grow more crystals from a treated seed crystal, an environment or medium must be conveyed for them to grow on. This is usually a substrate, a building material such as porous brick, a hard sponge or some rocks. This germinates a crystal garden, growing many times larger than the seed crystal. When this naturally occurs in nature, usually in some hollowed volcanic rock, it's called a geode.
Forming Large Crystals
Growing large crystals takes longer than creating a simple crystal garden, and usually requires a much longer soak in a saturated (or nearly saturated) solution. One thing to avoid as much as possible is vibration. Agitating a growing crystal causes nucleation, which may not stop the growing process, but may cause many small crystals to form instead of one large crystal.