The AGP was more or less housebroken when we got her. She's not real reliable, but she will generally indicate when she needs to "go Poopie" by walking over to her T perch or leaning towards it... if we're paying attention, we'll give her a lift. (She squats a bit and waggles her tail before she goes, but by the time you see her doing that, it's too late to move her!) Otherwise, we put her on her perch every half hour or so and tell her to "go Poopie" and she does!
I have read of people teaching their birds to, for example, stay on their playstands and not climb down, but my understanding generally is that you can't teach a bird that certain areas of a house are off-limits. My experience with the AGP, who is as independent as a hog on ice, indicate that a Grey's going to go where s/he wants to. The key, therefore, is to make areas the bird can get to bird-safe: You can't count on teaching a parrot to leave certain plants or the electrical cords alone, or to stay out of the kitchen or bathroom.
Alex is probably the best example of a Grey's trainability, but then, he was an exceptional bird.