Like any mineral in Stardew Valley, fire quartz needs to be foraged out in the world rather than made yourself. The Mines are where you will need to spend your time searching, but only after you ...

You can also find it inside Fishing Treasure Chest, and occassionally in Trash Cans after you reach the bottom of the Mines. You need 1 Fire Quartz to make both the Slime Egg-Press and the Dehydrator.