If you have an amethyst, follow these tips to make sure it's authentic. Generally, amethysts are not fake because they are inexpensive gems, however it would be best to make sure.
Steps

Step 1. Evaluate the retailer where you bought the amethyst
If you bought the amethyst from an authorized dealer, find out about the gem and where it was extracted from.

Step 2. Keep the amethyst on your forehead
If it is authentic it will stay cold, otherwise it will immediately become the same temperature as your forehead.

Step 3. Try scratching it
The gem is authentic if it manages to scratch a porcelain tile, with the same degree of hardness, i.e. 7, 0.

Step 4. Do the smear test
Being a variety of quartz, amethyst scratched against porcelain will produce a white colored smear.

Step 5. Check the color
Amethyst is a deep purple color with different shades, such as purple-white or darker purple.

Step 6. Check for any imperfections
A fake gem will most likely be totally free of imperfections, while an authentic one will have minor ones.