How can you teach your budgie to not be scared of you and sit on your finger?

Taming a parakeet takes some time. Before you can get them to sit on your finger you have to help them to not be afraid of your hand. I would suggest a few times a day putting your hand in the cage, close to them, but not too close if they bite. Eventually they will realize that you are not going to hurt them, and will become used to your hand. Also when you feed your budgie don't take the seed dish out of the cage, except when you are emptying it. They will learn that your hand brings food as well. Once they are used to your hand, talking in a soft voice with your finger just in front of the belly say up and lightly push your finger on their stomach. If they do it then praise them, if they try to bite, use a firm voice and say no, remove your hand and try again a little later. They love the attention and when you talk firm and then leave them alone enough they will learn that what they are doing is wrong. They can understand the tones of your voice. They are part of the parrot family and are very intelligent, it just takes time, everyday to tame your budgie. Once the will get on your finger a few times and you are able to take them out of the cage, that is if you keep their wings clipped so they don't fly into something and hurt themselves, put them on your finger and use both hands right index finger, then left, then right as if they are climbing a ladder they will learn when you place your finger on their tummy you want them up. I once heard that because hands are large it is intimidating to them unless you slowly introduce them to your hand. Best of luck to you.