"Cut and refine fine Gems from raw Crystals"
To begin you will need to mine Amethyst, best place for starters would be at Othalo Mine,
east of Eldevin city, exit through East-North gate.
Way to Othalo Mine
Look for Amethyst Deposit's inside the mine and mine with your pickaxe.
You will usually get:
After that find the Crystal Cutting Bench (one is in the Othalo mine, near the entrance) and buy some Abrasive Polish from Kerem (he is close to the bench)
Kerem and the Bench
Using the bench will open the crafting window, choose Amethyst Stone (you can do only this one at start, of course) and then click on Refine.
And there you have it, you just made your first Amethyst Stone in Eldevin.