It would depend on what type of animal it was and what type of entertainment it would be providing. A list of animals that took part in events can be found on this page.
Some animals such as zebras and ostriches were trained so that they could pull chariots. Other animals were taught to do tricks. With the massive variety of animals that participated in the many events some were used just for "hunts" or pitched against a gladiator in a fight to the death.
The more exotic animals that were used in "hunts" or pitched against a gladiator in a fight to the death were probally wild animals with no training.
Also, some gladiatorial events involved releasing herds of animals into the arena just so they could be slaughtered. There would have been no point to train these animals.