I'm new to bird owning but thought I could help with this (more experienced owners, check me on this):
What I did for my new bird (I got her yesterday) was use a previously untouched planner, and I filled it out with what I would need to do do get my bird fully tamed. This way, she will have a very easy transition and hopefully won't end up being very skittish or shy. My planner is filled out kind of like this...
DAYS 1-3 or 4 (the longer the better)- Get the Budgie used to you. Only touch the cage or be in close contact when changing the food and water. Read/sing/whistle/make random noises around the Budgie to help get him used to you. It also helps to play soft music or a youtube playlist of chirping budgies. This is the time when the Budgie should be adjusting to his new environment.
DAY 4- While talking softly, place hand on side of the cage for 10 minutes, twice a day.
DAYS 5-6- Rest hand on the bottom of the cage for 10 minutes twice a day. On day 6, introduce him to spray millet by leaving it somewhere in the cage.
DAYS 7-8- Rest hand on a perch or closer to the bird for 10-20 minutes, twice a day. If the bird flies away, keep repeating this until he doesn't.
STEP ONE (because it may take multiple days to accomplish)- Get him to eat millet by hand.
STEP TWO- hold some millet on the other side of a portable perch. Place this in front of the bird. If he wants millet, he will step up onto the perch you are holding to eat it. When he does, say "step up"
STEP THREE- Once he is used to perching on command, slowly move your finger down the wooden perch until he is sitting on your finger instead. Then you can remove both the treats and wooden perch to get him to "step up."
STEP FOUR- Have your budgie "step up," then SLOWLY remove from the cage.
As long as you take this whole process very slowly, your Budgie will have an easy transition into your household and hopefully won't be too skittish etc. Be sure your budgie doesn't get out of its cage until it's tame,or it can be stressful or damage your relationship if you have to catch him to get him back in the cage. I hope I answered your question
