So I don't know much about working with deitys, but I've seen people mention "feeding" them. How do you feed a deity, or what do you do with the food you leave on an alter?
Basically yes, you feed them food. Many people have a plate on their altar that they use to place offerings to the gods they follow. Some even go so far as to set a place at the table for the gods and serve them food as they do the rest of the family.
Now,there are two different ways to deal with the food after. Some throw it out. Others, consider that as the gods are etheric, they have taken what they need and the food is permitted to be eaten by those at the table.
When feeding dieties, be sure to research the likes and dislikes of the diety. It is counterproductive to offer food that is disliked, so care should be taken to make sure it is acceptable. Bread is usually a safe thing to offer if you are unsure. If you are to the point in your relationship with a diety that you can ask them what they want to eat, then that is the best way to know what they want.
Offerings can be left for deity upon an altar which feeds the deity spiritual energy. Offerings can also be left in other ways and in other spaces depending on the magical working. A libation poured upon the earth would be one way of feeding a deity as would leaving an apple upon the altar at Samhain. Spirits and deity can be feed simply through our own energy as well. Our prayers to a deity feeds them our energy possibly invoking the deity depending on the verbiage used. Aligning with the spirit or deity's likes in regards to offerings does help but many spirits whom are know for certain attributes such as patience, forgiveness, kindness, and peace will see the truth behind the offerings one has to give
i used to have meals in dedication of my deities, specifically when i worked with loki. i would find a meal to the best of what i had available that i felt was suitable, go outside, call out to them and proclaim the meal in their honor. usually id set aside a portion for Loki and when i was finished id either put the remnants in the earth or eat it myself. ive found this practice to be exceptionally beneficial for creating bonds with deities, as Loki would often join me in the form of an animal or an astral form.