Most creatures in the mod are simply tamed by imprinting on a player that is standing within a few blocks of the animal when it hatches/is born.
If a player mistakenly misses this event, and the creature is untamed, they can also be tamed by feeding them by hand, or by using a whip, and as a consequence, the poor animal will lose his mood. You monster.
For larger land predators such as Tyrannosaurus, Allosaurus, and megalania, this method will not work. Instead, once the creature reaches an adult stage, you must get the creature on to low health (when it falls onto the ground, visibly unconscious), and give it a Scarab Gem. It is best to do this carefully so that you do not accidentally kill the creature.