Here is a step by step process to tame your budgie.
This step is especially important if your budgie is new. Before you attempt to tame it, let it get accustomed to its new surroundings.
When the budgie has settled in its new home, you can start by just holding your hand out and placing a finger on the cage.
Take your taming session to the next level by putting your hand inside the cage. Keeping talking to the budgie in the same soothing voice.