Hunting for animals in SCUM can provide you with materials for crafting, a chance to test your combat skills, and most importantly: Food.
You can get meat from killing zombies and other players, but nothing is more nutritious (and better for you) then resisting the temptation of cannibalism and sticking to the meat of the animals. Thankfully, there are plenty of animals to hunt in the game throughout the map. Assuming you know where to look.
The developers are also looking into ways to tame animals for companions. Brushing up on these skills now might get you closer to a Bear ally in the future. Nothing is concrete at this time, but it is good to dream.
To hunt, make sure you have a sharp object, like a stone knife, to skin them for their meat.
Animals will only be found in woody or grassy areas. If you are looking for a deer or a bear near a town, you'll be out of luck.
You can see animal tracks on the ground when an animal is nearby. These prints are usually small black spots on the ground. If you took points in awareness skills when creating your character, it will increase the likelihood of finding and seeing these tracks.
Animals will always make noises when you are near to them. Be sure to keep your ears tuned for distinct sounds. You can mute other sounds in game by holding down the right mouse button to enter Focus Mode, letting you hear animals over the game's ambient noise.
Now that you've found Bambi's mom, it's time to kill.
While you could run towards an animal while out of its sight-line, swinging frantically in hopes of chopping it down before it has a time to react, you're a lot more likely to make it flee. Or worse, have the tables turn and get a chunk taken out of you instead. Some animals will try to attack you if provoked.
It is better to craft a few throwing weapons like an improvised spear, or have a gun to take out an enemy from afar.