It totally depends on the bird.
Both Piper and Shade I got as babies so there wasn't too much of an issue with either of them.
Joey I got just shy of his 3rd hatchday and he had a great owner and life before coming here and the moment he was here he wanted out and to explore, which I loved since I was told that he normally stayed in his cage a few days before heading out when he used to go at his old birdsitter. I took it as an extreme sign of his confidence in us

Petey....ah Petey. I took Petey in with the knowledge of him hating women. I had a great month of "honeymoon" and then, as suddenly as possible, he got really bad with me.
Now, I got him two years ago so he would have been 13 and he is still learning what toys are for. It's a very very long process, but he's getting the hang of it. I keep offering toys and let him go at his own pace.
Zuri. Was still very young when I got him (just barely one I think) and took to toys right off the bat. Adjusted fairly well, his trust in me grew quickly but trust in my boyfriend took longer. They are still working on it and it's getting better. Still is a picky eater of fresh stuff but is getting better as well (and I've had him for over a year).
Pixel. Didn't seem to know what toys were for and after a few weeks started to figure it out, although she isn't quite comfortable with all of the different kinds, she is starting to be "braver" about them. She also, after a little over two months, seems to be getting a bit more comfortable here but is still rather afraid of my boyfriend.
So with all of them the "adaptation" period was not the same. It really depends on how old they are and what their life prior to coming to live in their new home was.