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Other Quartz
Amethysts are often found near other stones from the quartz family. Citrine, a yellow-colored quartz gem, is commonly found in combination with amethysts. Amethysts are also found on top of clear and cloudy gray quartz. Irradiation from the sun or surrounding elements causes the chemical change that turns amethysts purple. Neighboring quartz that isn't exposed to the irradiation or doesn't have the necessary manganese and iron to cause the purple coloration will not become an amethyst.
Geodes
Amethysts form in long, prismatic crystals. The most prized place for collectors to find amethysts is in geodes, or hollow rocks filled with crystals. Geodes form in cavities of volcanic rock. As the rock cools and hardens, it's filled with hot substances for the surroundings--gases, mineral-saturated water and volcanic material--causing it to be hollow. As it cools and the substances distill out of the rock, the minerals in the water crystallize. The right minerals and water temperatures form amethysts.
Volcanic Rock
The largest amethyst concentrations are found in volcanic rocks, according to The Quartz Page. These deposits are found all over the world, but the largest deposits are in Brazil and Uruguay. Prior to South America's rise as the top producer, most commercially mined amethysts came out of Russia and Siberia.
Metamorphic
Although most amethyst deposits are found in igneous rocks, The Quartz Page says amethysts are also found in metamorphic rocks. They are rarely found in sedimentary rocks, because the chemical conditions necessary for amethyst formation aren't generally found as sedimentary rocks form. Amethysts are found around the world, but their look and shape is different depending on where they are mined.