In general crystal is produced by a crystal manufactory. You can buy them from the wholesaler using either coins, supplies or some other goods (I forget which).
But, your question, if I'm reading {into} it right, is about diamonds, (which you call "crystals.") If so they can be purchased with real money. Other "free" sources are: buildings which give diamonds (you can win these if you are lucky, in events or at some points in the Spire). The Spire gives out some diamonds (if you are lucky), and the crafting allows you to sin some diamonds. Craft and do the Spire regularly and you can get diamonds or diamond producing buildings.
AJ