Minecraft wiki entry for The_second_day, associated text: You can kill a few animals upfront, but they'll run out quickly, and you need to save some for breeding. Again, cooking the meat makes it more nourishing.
Wheat takes a day or two to grow, as do other crops when you get them.
If you have a fishing rod and a safe place to fish, fishing is a great way to get food, because it doesn't involve fighting, mining, or moving around much. Once you have a fishing rod and a furnace in which to cook the fish, you typically don't need any other source of food. Campfires are even better for this in the early game because it has a cheap crafting recipe and uses no fuel. Putting a hay bale under it creates a smoke signal that you can see from a distance. If near a river or ocean, you can alternatively slaughter cod and salmon mobs with a sword, as they can abundantly spawn and it's a faster way to gather fish than rod-fishing. You can smelt your first few fish while you fish for more.
Dried kelp and sweet berries are easy to obtain, and can restore your food bar if you have enough. Watch out for those sweet berry bushes, though, and drowning is bad too.
If you're desperate, you can try breaking oak leaves or dark oak leaves for apples. Using a hoe allows you to break leaves a lot faster. Be careful to not take damaging falls or jump around a lot in the process, much less get attacked by monsters.
If you are really desperate you can also eat rotten flesh dropped by zombies, but this usually gives you food poisoning, a.k.a. the Hunger effect, which would drain your hunger by almost as much as one piece of rotten flesh fills it. The trick is, if you have a lot of rotten flesh you can quickly fill up on that, then tough out the food poisoning and end up not too hungry.