Taming a pet budgie is all about gaining his trust. You are much bigger than him, and his natural instinct will be to feel intimidated. It takes a little time to reassure a young budgie that the hulking monster beyond the cage is not only harmless, but is a friend and playmate too.
Sudden movements, loud noise and banging things against the cage will frighten your budgie, no matter how happy and extrovert he seems otherwise. Sticking a hand inside the cage will spook him too, so things have to be taken slowly.

Gaining your budgie's trust is the key
Taming Budgies Together
The tips that follow apply largely to smaller cage setups of up to four birds. Taming larger groups – in an aviary, for example – is a different, and far easier, proposition, as you will not be training them individually. Unless you are setting up a new aviary, there will be a few birds already used to your presence. The newcomers will learn from this and come to see you as harmless. Linger with them for any length of time, and they will begin to use you as a perch.
If it is a new aviary, lingering with the budgies is even more important. It doesn’t have to be inside the cage, but make sure you spend a few hours each day close to the bars, talking and moving around so that the budgies can watch and, ultimately, ignore you. Make sure other family members and pet dogs show themselves too.
Taming a Budgie Fast
Taming individual birds requires time and effort. If you want to tame a budgie fast, you’ll need to hold several training sessions each day. That way, you might have a hand-tamed bird in a week or two. The more time you put in, the fewer days or weeks it will take to gain his trust.
Building trust is the key – this is the first step, whether you’re attempting to get a budgie talking, perching on your shoulder and performing a couple of tricks, or simply aiming for a cageful of birds happy with your presence.
Andi, 24 June 2019
I recently rescued 2 males. I had to reach inside their cage to catch one of them due to having an over-grown beak issue. I then had to seriously clean their cage, as it was in dire condition. It did freak them out for a bit, but I think they know what I was trying to do for them??? After cleaning their food dish (which was gross and caked up), washing out their water container and cleaning out all the yucky, I put in 2 blackberry bramble limbs from my garden and they seem very lively. I've had them for 3 days now, I talk to them, sing to them and watch them...how long do you think it will take for them to trust me? I've loved birds for my whole life (46 years), but this is my 1st time owning any.