Food pops at the beginning of each day/turn. Assuming the side can pay for the upkeep of its units, every unit will automatically pop enough food to nourish it for that day. Food appears already cooked and needs no preparation.
Units, including Royal and noble units, and presumably casters as well, all pop in cities after a certain period of time. Warlords can be popped, but doing so takes a long time, and as they can be designated, or promoted, from regular units, this means that the length of time needed for popping a warlord can be put to use popping normal unit.
Units can pop at random outside of cites as barbarians.