Killing animals is tricky because the majority of them will either run away faster than you can chase them or fight back with often fatal consequences. Even boars can kill you if all you have is your rock. If you manage to kill an animal, for maximum yield, butcher it with a bone knife which you can craft for 30 bone fragments.
Depending on their size you’ll get a varying amount of animal fat which you can combine with cloth to craft low grade fuel which is a vital early game resource.
The easiest way to kill an animal is with a hunting bow and the easiest animal to kill is a boar. They give you lots of meat and animal fat and they run at roughly the same speed as you so if you hit one with an arrow, you can chase it and with practice land a few more arrows in it.