Taming a wild bird is a considerable undertaking. Since birds make wonderful companions, it is worth the effort. To accustom a bird to handling, you actually have to handle the bird. This can be dangerous and often is the reason people don’t succeed. But a bird who accepts handling will be more relaxed living around humans. The taming process can take a few months. During these months keep the bird’s flight feathers trimmed. 

Canaries and finches can be tamed to ride on your hand by patient hand feeding in the cage. Your presence near the cage at feeding time and later with your hand on the dish at feeding time, can desensitize the birds to your presence until they readily stand on your hand. Once they do, special treats reinforce standing on you for longer and longer periods of time.

For larger birds with dangerous beaks, you will need a training area outside the cage. Remove your parrot from his cage with a soft towel so that he cannot bite you and he does not crash around the cage. At first, this may be difficult but it is important that you become skilled at toweling your bird so that it is not traumatic and so that you can do so in an emergency. You may choose to keep your bird in a smaller cage during the taming process so it will be easier to catch him gently.  If you wear gloves to handle your bird, be sure you are not squeezing him. Birds breathe using the muscles on the outside of the chest. If they are held tightly around the chest, they cannot breathe. 

Take the bird to another room away from the cage to the training area. It is important that you work in a room without other animals and without much furniture. It will undermine your bird’s trust in you if you chase him around objects in order to handle him. 

Place your bird on a secure perch and have some special treats your bird does not usually receive, such as sunflower seeds or grapes (bird favorites). You want your bird to look forward to his time away from the cage and to see you as a source of good things. The first day, offer the treats in a dish and sit in the room and read. Return your bird to his cage. The second day, offer treats from your hand. Your bird may take the food only to toss it on the ground. Persevere. During the taming process, never deprive your bird of his regular food which should always be available in his cage. Save a few favorite treats for your time together.

Once your bird begins eating food from your hand, offer him your arm or a stick firmly against his lower chest. The perch you offer must be slightly higher and in front of the one on which he stands. Birds will seldom step down for any reason other than escape. If your bird escapes onto the floor, offer the perch again. A bird is more likely to accept a ride from the floor than from a safe perch. Once your bird readily steps onto an offered perch, add a word that will let him know when to do this. Many bird owners use "Up" or "Step Up". In fact, many birds say "Up" themselves. When he steps up, transfer him back to his safe perch and repeat. 

A bird may want to test the perch with his beak before he steps onto it. This may not be an attempt to bite so be sure not to move the perch while he is testing it out. 

When your bird readily steps on the perch when you ask, offer a long lasting treat as he steps up to encourage him to stay on the new perch.  Begin moving your free hand close to his tail and then his feet. If he grabs at your hand, wiggle his perch slightly. If he stops, reassure him with your voice. He wants security for perching and will learn that biting is risky. NEVER cause your bird to fall from his perch. His growing acceptance of handling is based on his hope that you can be trusted. 

Eventually, rest the perch in your lap and accustom your bird to being touched and fed by you. Birds enjoy having the feathers on their neck gently ruffled and especially enjoy gentle circular massage near their ears. 

If you are able to work with your bird for 5 minutes twice each day, the entire taming process will take a few months. Patience is truly a virtue when working with birds and the friendship of a bird is truly a gift. There are several good books on Parrot training that you and your family may enjoy. I recommend books by Mattie Sue Athan or The Pleasure of Their Company and My Parrot My Friend.