Alright, I am back to help you with how to start taming your budgie.
This is in addition to spending a great deal of time just hanging out in the same room as your budgies is in so that it can get used to you being there and not being afraid that you will eat it. Set aside two or three periods of 10 minutes each, once in the morning, one in the middle of the afternoon and one about an hour before dusk or dinner time. Skip the on in the middle of the day if you want to. Start with some sprig type of millet, it looks like seeds on a stick, you want it so that you can offer your bird a treat during these sessions. Start from across the room from your budgie and just call out the birds name so that it knows that you are talking to it. You are calling it a he so I will also for the remainder of this. Call his name and watch him from the corner of your eyes and not a full direct stare type of look as that is how a predator looks at a bird and you don't want him to think that you are looking at him as a snack. start talking to him, use a soft coaxing type of voice and while talking to him in this manner be sure to use his name a lot and give him lots and lots of good bird type of praise and encouragement. Look to see when he is relaxed, and start moving towards his cage, sort of meandering around the room kind of like a creek does through the landscape always coming closer and constantly talking to him and watching his so that if he starts getting nervous you can stop approaching until he relaxes again. Only move closer when he says that it is ok by relaxing. I know that this is time consuming, but taming is all about establishing trust. It might even take a couple of sessions until you can get all of the way to the cage using this manner of approach but it is worth it in the end. When it comes to your bird trust is everything to it. When you make it to the cage, still talking and praising your friend offer him a couple of bites of the millet through the bare of the cage at the perch he is on. He might come right over and take a bite or two or he might not. If he does not take any then just break off a small piece of the millet and place it in his food dish. Continue talking and praising him and offer him another bite of the millet in a couple of minutes. Again it might take a few sessions like this before he comes to take a bite of the millet, but be patient with him as you are building a foundation for your relationship with him, a foundation of trust. When the session is over and if he is not taking the millet from you through the bars of the cage be certain that before you walk away that you break of a piece of the millet and place it in his food dish.
Let us move on to where you are able to walk up to the cage pretty much directly. What you want to see is that not only can you walk directly to the cage but that when you call out his name at the beginning of the session he responds by coming towards you in anticipation of your coming to him. this is the first sign that this is working to build his trust in you and an indication that he wants to spend time with you. Now when he begins to take a bite of the millet through the bars of the cage, what you are looking for is that he comes over to get his treat when offered but he also takes it calmly and remains there while he eats it and then calmly takes and eats a second bite. These are also signs that his trust in you is growing. When you see these things from him for at least two sessions it is time for the next step of the taming process. Now when you approach the cage talking to him go to the main door of the cage and when you are directly in front of it, open the door and stay directly in front of it. Talk to him just as you have been doing and when it is time to offer him his treat do not reach in the cage. Offer the treat only right at the entrance to the cage and no place else. Since he is probably on the perch that he has been being on when you offered him a treat through the bars it is very tempting to reach into the cage to offer him a bite of the millet, but that is exactly what you do not want to do. This is still all about gaining his trust and he needs to come to you and take the treat from you directly at the cage door.
In order to help him with this you could place a perch just under the main door to his cage now, even before you begin these sessions so that he gets a chance to get used to it being there and is not afraid of it. When he comes over and takes his treat directly from you at the cage entrance and calmly eats it and does the same for a second bite you have two things that you can do next.
These two thing can be done at the same time, so to speak, as one does not need to happen before the other. The first is to use two hands at the cage entrance, one to hold the millet and the other to use as a perch for him. for this you continue just as you have been doing, but now you hold the millet so that your friend has to either step up onto your hand to eat the millet or he must stretch a bit to reach it to take a bite. you don't need to do anything else with this that is different than you have been doing. Just be patient and he will begin to step up on his own to get his treat, but it is a very major step in trusting you for him to do this. Just be patient and when he is ready he will start stepping up.
The other thing that you can do is to begin a different training session in which you begin to teach him the basics of targeting. here is a link for you that will teach you what you need to know and do in order to do this.
viewtopic.php?f=11&t=227 This should help you in the areas that you have asked about. Take your time and enjoy the process and your new budgie friend. Thank you for allowing us to help you with this.