To survive in Haven and Hearth, you need food. To get food I advise the first skills you learn are "Hunting" and "Foraging".
Now go find a rat or a rabbit. To catch either, get up right behind them, turn to the fastest speed you can, and right click the animal. They should appear in your inventory if there is a 2x2 space. Right click a rabbit and click "Wring neck" then right click again and click "Butcher" build a fire and cook the meat.
For a rat, get a stick, make a fire and have a good ol' rat on a stick.
For the players who get sling but are still not ready for melee, get the skill "Boat building" construct a boat, and cruise down the river until you see a boar or a fox close by. (If you want you could try bear, but you need a high Q sling) make sure your marksmanship is at least 9. Get as close to the animal as possible without it being able to attack you, when you are ready to fire, wait for the animal to "Twitch" first. Doing so will prevent them from running away. Once killed, if you want the skin, hit "Skin" first or the skin will be lost. (You need a sharp tool equipped to skin animals. Stone axe works fine.) After you skin the animal, you can butcher it for intestines and meat. If you want, collect the bones. Make sure there is a container like a crate in the boat.
With the foraging skill you can go around and forage food like blueberries, spindly taproot, etc.
Good luck finding your food!