There are various species of animals in various points of the map. Information about species living in a given area can be obtained after you destroy the coder inside the box, at the top of the radio tower.
Each animal you kill can be flayed, and materials thus obtained can be used to create new items, like bigger rucksacks, holsters cartridge belts etc. If you do not encounter an animal that you are looking for, in a given area, walk away from the area and return after some time. The time of the day has no bearing upon the appearance of animals in a given region.
As far as hunting sea animals is concerned, you need to use boat and swim out to the areas in which these animals live. As soon as you spot the specimen that you are looking for, shoot it while on the boat, and jump into water to flay it. Dead bodies will be falling down to the bottom so, you need to hurry. You can also try and kill a given animal while on the beach, provided the animal swims up sufficiently close.