Main write-up can be found here.[]
Items (Artifacts, Ingredients, and Stones) can be consumed in the Hall of Artifacts.
After you reach a certain inventory score threshold (effectively number of artifacts currently in one's inventory), a tutorial pops up, showing where the consume icon is, and directing you to consume something. After an item is consumed, it no longer appears in your Hall of Artifacts, and a small popup at the top middle of the screen indicates the items returned in exchange. These are generally either Golden Eggs, or stone fragments.
You can consume multiple of an item at a time by pressing the recycle button and then holding down the red button that appears (which you would usually just tap to recycle 1 of the item). This brings up the Multi-Consume menu. From there, the red button will Cancel the multi-consume, the yellow button will consume 50% of the that type of item (the amount CONSUMED is rounded down if it is not an integer), and the green button will consume 100% of that type of item. Multi-Consume does not work with Rare/Epic/Legendary Artifacts, since they are listed separately in the Hall of Artifacts. Multi-Consume also does not work with items of which you have less than 10.