Well, I've read about people who've hand reared chicks that loved to sleep in their owners hand, even when grown, but if the birds haven't been used to this kind of thing all their life, I think it is hard to achieve that level of tameness.
I haven't really tried to tame my birds, but I have been collecting bugs around the house and given those to the birds, and it didn't take long(like, 2 bugs or so on the ground beside my hand) before they would take them out of my hand.
I have my breeding buttons in an aviary and while they were incubating eggs, I entered the aviary daily to remove the huge poops they make when they are incubating. I moved around slowly and they were more concerned with getting close enough to see whether I found something edible in their bedding, than with making sure I didn't step on them. Their chicks seem even more confident around people, possibly because they have been used to my presence since they hatched. The parents raised them, but I have spent hours looking at them, trying to get good pictures of them and so on. But in general, my buttons don't like being touched - they will keep a distance of ~10 cm if I put my hand towards them, even if I do it slowly. However, if bugs are involved, they don't mind covering the last 10 cm themselves, after a few seconds of considering.
I could probably get them tamer - maybe make them step onto my hand to get bugs - if I spent a little more time trying, but I'm happy with them just not being scared of me, as long as I move slowly.