@alleyj
The thing with training any animal is that there is no 'one set of rules'. Not every method will work with all animals. If the method isn't working, that says it right there. It's time to try something else.
Some say timeouts don't work because the bird doesn't know why. Personally, I disagree. In my experience, birds are a LOT smarter than we think and love to test boundaries. Timeouts worked wonders with Skittles. I bought him a 'timeout cage'.
First thing I would due is determine WHY he was screeching. If it wasn't because he needed something (food,water,bath) but rather just acting out, thats when the timeouts came into play. When he would start to misbehave (in terms of excessive vocalization), I'd give him an initial warning. To start off, he had three chances. On the third time, he'd go into his cage for a timeout. If he continued to act out (while in his cage), I'd cover him up. If he still continued, I'd put him in a dark room for 5-10 minutes (until he calmed down). I would take him back out as soon as he calmed down. If he started up again, I would immediately put him back in a timeout.
With regard to biting or over-aggression. I give Skittles warnings on bites (he is usually responsive to the command "no biting") but if he wasn't, I would do a timeout. With regard to the over-agression etc, you gotta go directly with timeouts. As soon as they are doing that, you put them back in their cage.
Some may disagree with my methods, or the manner in which I practiced them but they worked wonders for me and Skitty. Note, he doesn't have a timeout cage anymore and I cant remember the last time I had to give him one (its been months, if not several years). That's not to say I haven't had to put him in his cage for misbehaving from time to time, but he no longer needs a timeout cage.
I think him having a 'timeout' cage was one of the biggest factors in his success. It was used primarily for that purpose. Not for vet trips, not for outings and not for sleeping. ONLY for timeouts. That way he knew what it was for.
Truth is, some suggestions people have made would not have worked with Skittles and some of my suggestions may not work with others. You have to find what works with your bird by trying different methods.
Ultimately, the biggest factor in whether a training succeeds or fails falls on patience and persistence. You HAVE to set limits and boundaries and you HAVE to be 100% persistent with them. I cannot stress that enough. They will test those boundaries, even after training them. Skittles does this, he tests his boundaries.
Now, as for the positive parts. Parrots love attention and love positive reinforcement. Use cutesy words and praise your parrot when he is behaving. Even if you are not in the process of training him. If he is just going about his day and behaving, praise him. I do this with Skittles and I give him treats throughout the day. He doesn't get them if he is misbehaving and he loves his treats!
Again, persistence, patience, boundaries and limits.