To prevent death by starvation, it is vital to regularly consume and enjoy several foodstuffs every day. Eating food restores large amounts of energy and sometimes minor amounts of hydration.
Commonly the first source of food, both for early homo-sapiens and your in-game character, gathering local fruits and vegetables in the wild can sustain you until you find more stable food sources. As of now (early access 1/17), this only includes blackberries, which grow in abundance almost everywhere outside urban centers.
Before the apocalypse, Americans had access to copious amounts of food, some of which has survived in the abandoned structures of the valley. Currently (early access 1/17) there are several types of pre-Zombie foods that can be found just about anywhere, but they all appear as a plain tin can.
While not exactly the simplest way to obtain food, hunting the local wildlife to extinction can be rather enjoyable. There are currently (early access 1/17) four local food-yielding critters that can be hunted; rabbits, deer, wolves, and bears. After them, the creatures can be skinned with a bladed weapon, yielding 1-3 units of meat and sometimes some other useful crafting materials. These meats can be consumed raw, or cooked over a fire. Raw meat can cause food poisoning and does not restore as much energy as when it is cooked. Rabbit meat may also be obtained through traps.