Summarize the following:
Once your parakeet doesn't move away from your hand, it's time to do the same on the inside of the cage. Reach inside your budgie's cage and rest your hand there for a while. It's especially effective if you do this while holding a treat, such as millet. Holding a treat helps to gain the bird's trust.  Slowly, over time, move your hand closer and closer to your bird. Chances are, if you are holding a treat, your parakeet will begin to eat from your hand. If you coax your budgie to a place in the cage where he or she cannot reach the treat in your hand while on a perch or the side of the cage, your budgie will likely be convinced to jump onto your hand to get the treat. After a while of feeding the bird on/from your hand, try to get your budgie to perch on your finger without food by slowly approaching it with your finger and nudging it against their belly near the feet. Your parakeet may jump off your finger quickly, but keep trying—just don't overwhelm the bird. Give him or her some time between attempts and continue to move slowly. Be patient, and your bird should start getting on your finger voluntarily over time. The next phase of hand training is getting your bird to come outside the cage while perched on your hand. Because your parakeet feels safe inside the cage, he or she may jump off your hand near the exit. Keep trying, though, just like when you tried to get him or her to eat from your hand or perch on your finger. Eventually your budgie will learn to trust you enough to come outside the cage with you.

Summary:
Approach your budgie from inside the cage. Get your parakeet to perch on your finger. Bring your budgie out of its cage.