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The purpose of each of the 24 levels is to earn enough money to reach the money goal for the level. When you succeed, you move on. When you fail, you replay the level.
The customer's order comes in a thought bubble. For artifacts, just tap the item and tap the customer and that's it. The customer leaves cash behind and you need to pick it up or you don't get paid. Another customer may request the same artifact, but you can only have one on the shelf at a time. So after selling an artifact, Lilly needs to tap the shelf for a replacement.
But most orders won't be as simple. When you receive a potion request, you need to tap the ingredients and tap the cauldron to drop them in. After the potion cooks, tap the cauldron to grab it and deliver it to the customer. Occasionally you'll need a feather from a phoenix to complete your potion and you have to wait for the phoenix to produce one after tapping the bird.
Sometimes you need to grow an ingredient on a plant. The plant needs ingredients to grow. Tap the needed ingredients and then tap the plant. The plant lets you know what it needs until it produces the special ingredient.
Between levels, you can buy upgrades for the store. These include faster cauldrons, extra storage for completed potions and something to help customers be more patient. Also a mini-game pops up every few levels where you match at least three of the same object to earn more charms.