How to Tame A Cockatiel. Part of the series: Pet Birds. Taming a cockatiel involves teaching it to step up on a finger when ordered, to stop biting using the blowing and bouncing technique and to make sure they know that they owner is in charge. Tame a cockatiel to create a well-behaved and friendly pet with information from a pet hobbyist in this free video on pet care. Read more: