When you "use" a crystal, you open a box where you add the ingredients. Like in my recipe above, you "use" a water crystal, then pick from your items; distilled water (1), Wijnruit (again spelling lol) (1) and San d'Orian Grape (1). Pick "ok" and your lil fella will squish it all around and either succeed (yay, a home-made antidote!) or fail, where you lose the crystal and possibly some of the other ingredients.
Yes, you can mine, harvest, log, fish (YOU can fish. Me? No thanks.), excavate, and when you get your license, chocobo dig. When you get bigger, you can go clamming. I used to harvest a lot for cooking supplies. A friend also harvested for clothcraft supplies. We'd just swap the stuff we didn't need to each other. I decided to do cooking to save myself (and my sushi-eating hubby) tons of gil. My cloth-crafting friend is looking to get rich (lol). Youngun has worked a bit of everything because she's addicted to ranged attack and needed to be able to make her own bolts.