If a cockatiel hasn't been hand-raised it will take time to tame, but gentle perseverance will produce the results you're looking for.
I have two youngish cockatiels, a male and a female. Because they have each other for company, that has added to my considerations when taming them but here's how I've managed.
Cockatiel Taming Basics
For the first few days I kept my hands out of their cage except to change their water and food and foliage (I put willow fronds and other branches which they can chew on or play in). Whenever I went near the cage, I always said hello. This made me part of their flock. Always talk calmly to your pet bird while training it. They respond to calm confidence.
For almost the first three months I kept the cage closed but began to move my hand around inside it, adjusting things or just resting across a perch. Predictably the little birdies would panic and flap around a bit but when they realised my hand wasn't actually after them, they began to settle somewhere in the cage away from the offending intruder. Over a period of several weeks, they became accustomed to my hand and didn't mind being close to it though they steadfastly avoided contact. I also took to sitting very close to the cage with my whole body.
When I felt that my small parrots were thoroughly accustomed to my hand being in the cage without any harm befalling them, I began to leave the larger door open so my cockatiel friends could feel that they weren't imprisoned. They chose to ignore the open door but of course, it made it much easier for me to get my hand into the cage. I began to follow Jupiter, the boy and also the calmer of the two, around the cage. I never touched him, just followed him with my hand.
He scrambled all over the place at first but I persistently dogged him until he finally stopped, and then I would withdraw my hand. I did this for a few days, and as time went on he began to run more slowly from me. It became a sort of exercise where he led my hand slowly around the cage until finally he stopped somewhere. Once you start this exercise, I believe it imperative to not withdraw your hand until your bird stops. That way, it learns that when it stops, so do you.
Scratching your Cockatiel's Head
When I thought Jupiter could take it, I hovered over his head with my fingers without touching him, and asked, can I scratch you, then gently ruffled the tips of his plume. I always asked so that he would know what I intended. Can I scratch you, and then played with the tips of his plume until one day I was able to scratch his head. He allowed it, but the next day all I could get was the plume, and the same for the following day, but then, as long as he was in a particular position in the cage, he began to regularly allow me to scratch his head.
Neither of these birds was the typically curious cockatiel who investigates everything within range, usually beak first, so they didn't attempt to come out of the cage.
Getting your Cockatiel to Hop onto your Finger
Now that I was allowed to scratch Jupiter's head more or less whenever I wanted, and because he tolerated my hand close to him, I slipped my forefinger in front of his breast and nudged him backwards so that he immediately hopped onto my finger to avoid falling off his perch. This is the action birds engage in to stop themselves from being knocked out of trees by rustling branches. By reflex they merely climb onto whatever knocks their breast. At the same time as making your forefinger tap your pet bird's breast, give him the command, hop up, or step up, or up, whichever you want to use.
If you repeat this daily, eventually your bird will hop onto your finger on command without any need to nudge his chest.
Once I had Jupiter allowing me to scratch his head and hop up onto my finger, Chickie followed suit. A trick, if you're having trouble with getting your birdies on to your finger, is to use a spare perch as though it were your finger. Because your body is further away from the bird, it is less frightening for him and he will often readily hop up onto a perch. Over time of course, you slide your finger further and further down the perch until you can exchange it altogether.
Cockatiels will most often test anything they have to climb onto with their beak, giving it a little knock as if to assure themselves of its solidity before they trust their weight to it. They will do this to your finger too. This is not a bite and normally there is no intention to bite but if you get a fright you might spook the bird too, so be ready for it. It's a little knock with the curve of their beak, as we might test something with our foot before standing on it.
Enjoy taming your cockatiel. Remember patience and gentle persistence will win out. He needs to trust you and that can take time if he was not hand-raised.
