How do animals respond to their environment?

This depends on the animal. Different animals respond differently to the various stimuli they are exposed to. An animal that is naturally a prey-animal will run away when an animal that represents a predator (like a human, a dog, or a cougar). Or, if it's an animal that is protecting her young or a male protecting his harem (like a bull or a stallion), they will fight that predator that has the potential of destroying one or all of their herd members.

Then there's the environment. An animal will find shelter when it is raining or storming. They will find shade if it is too hot, or wallow in the mud or a water hole; others have the ability to perspire. They will huddle in a warm den or in a group if it is cold. They will travel to a water source of they are thirsty (there are some animals that are exception to this). Predators will hunt and kill an animal if/when they are hungry: a herbivore will travel to find their favorite browsing/grazing area to eat.