Player one should think of an animal. Player two then asks yes or no questions to get more information. For example: Is the animal you're thinking of a mammal? Does the animal you're thinking of have four legs? Does the animal you're thinking of have feathers? Is the animal you're thinking of a carnivore (eats only meat)?
If you want to make it harder, set a limit on the number of questions that can be asked before player 2 has to guess. Don't forget to take turns for who is thinking of the animal and who is guessing!