How do I make offerings on the altar and how do I make room for new offerings?

If when you try to add food to the altar or get a ready-made dish, you see the message that reads "There is no place", this means that all available slots are already occupied. To free up the slot, make a food offering on it. To make an offering, open the altar, drag one or more available dishes into an empty slot, and then tap the "Eat" button (plate icon on the right).
If you see the message that reads "Everyone is full" when trying to make an offering, it means that you have too much energy and a new offering is not available. In this case, you need to spend some of the energy before eating.

If you want to gain more energy, first make an offering, and then get energy from the chests/merchant's or Tia's gifts/energy packs.