First of all, when I left him to go work in my psychology lab today, he didn't scream. He's been screaming less and less when I leave for classes as well. I guess he's finally figured out that there is a pattern to my coming and going: when I leave at this time, I'll always at this.
Then I got home after working in the lab and I open his cage. Instead of flying to my hand and letting me carry him into the other room to his training perch to go to the bathroom, he flies past me, down the hall, into the living room, land on his perch and goes to the bathroom. Eureka! Then not ten minutes later, I reached for a banana and he instantly flew to the coffee table; ready for harness training!
Finally, just moments ago, he said his first understandable word, "hello."
I always let him roam freely while I'm in the shower because he likes to sit on top of the bathroom door and take advantage of the acoustics and the background noise to practice his vocalization. (He does a very convincing Logan. If I didn't know that Logan was in a different apartment, I'd swear it was him wolf-whistling and singing). Well, I turn the water off, step out of the tub, and Conrad looks down at me and greets me with, "Hello." 
He's not even four months old!Looks like my little boy is a smarty
Conrad- Senegal
As for getting him to just go on his own any subsequent time he's out of the cage, he's still pretty clueless. As for time, I've had him for a month and I was doing this on day one. You should definitely check out Michael's posts on the matter.
Rambo and 
Myrtle are both talkers, but whenever I hear the little voices say hello it just melts me. I realize that they consider Momma to be my name because that is what my daughter calls me, but I feel special when I here "Momma c'mere".