My budgie is picking up human speech very quickly. I started with one phrase, "fudgie-budgie" ...a nonsensical word just to make my 5yo little boy laugh. And I repeated it over and over, like 30 times at a sitting. My budgie likes to perch on my shoulder or sit on my finger with his head against my mouth. He looks like he's falling asleep, but this is really the best time to teach them a new phrase. They seem to pick up quickly when they are settled down and quiet. After about a week or so of this repetition, I heard him say it. I reinforced it by saying it again. Then I moved on to a new phrase.
Guido can say his name, "fudgie-budgie" "Guido is a good boy" and "here, birdie birdie birdie." We're currently working on "give the birdie a belly kiss." My dd said she heard him say it this afternoon. I've also heard him pick up fragments of conversations. I've heard him talk about members of our family and our computer.