When it comes to feeding your "Steve" the deeper you get into the game the more options you will have. Keep in mind that the better the quality of food the more quickly your Steve can recover. A good loaf of bread for instance can help you get back a little of what you lost well out hunting and fighting with monsters at night.
You make bread by harvesting wheat which you may have to grow, but can sometimes find wild.
You can also get eggs from the many chickens walking around and perhaps fencing them in. You can get sugar cane in the wild as well then craft it into sugar. In also helps to craft yourself a bucket it's easy to do, do you can then go to a cow and milk it. It actually is at much work as it sounds like but it's worth it on those long dangerous nights hunting down monsters, to help you recover faster.
There are fun things you can make too. You can also craft a pumpkin pie with eggs, pumpkin, and sugar, or craft yourself a cookie with coco-beans from a dungeon, or coco-plants from a jungle tree.
As you play the game at first you won't really be able to see if Steve is hungry or not. It's not like The Sims where there is an individual meter that tells you how he's doing hunger and sleep wise. You just have to watch the level of hearts and try to keep food on hand and rest when you can to keep those up.
You will learn quickly that poor Steve may not always be able to get sleep at night becuase monsters are to close. So food is a kind of on the go recovery method.
