Here we have a tried and tested method for training your budgerigar. Begin by putting your hand in the cage and offering some of their favourite food, millet, hold it in your hand so they can reach it and keep your hand below its head level. Do not put your hand in too quickly as you will cause alarm, if they do flutter about then it is important to keep your hand still and not make any fast movements or get alarmed yourself. If they are startled and flutter into a corner, keep your hand still for a couple of minutes then slowly retreat your hand out of the cage.
You should frequently offer millet to your budgie this way, you can do this every 2 or 3 hours if you have the time. Usually after a couple of days, sometimes sooner sometimes later, your budgie will feel brave enough to take a peck at the millet you are holding in your hand. Move your hand closer so that the budgerigar has to jump onto your finger to eat the millet, do not jerk your hand when they do so its important for you to stay very calm at this exciting time.
Once they have been standing on your finger eating millet, you can start to offer them your finger through the cage door without any millet and get them to use your finger as a perch. Slowly move your finger towards the bird, approaching them from below and stroke their lower breast with your finger, say its name or something like 'hop on' or 'step up' in a soft voice and if they are comfortable enough they will step onto your finger.
When you are confident that your budgerigar is happy on your finger inside the cage you can then move your hand out of the cage with them perched on your finger, do so very slowly ensuring they do not catch their feathers on the cage on the way out. You should always finger tame your budgie inside the cage before they are let outside of the cage, trying to catch a budgie that is not finger tame is very hard as they do not trust you yet and they will only get frightened easily.