Unfortunately, it takes a long time to fix screaming problems. You`ll need patience, and ear plugs.
The most important thing is to ignore screaming ENTIRELY. With two exceptions: alarmed screaming (if it sounds like he might be hurt or frightened, find out what`s wrong!) and when you just get home (give your bird a proper greeting and cuddle, even if he`s screaming, then put him back down and ignore him until he stops).
Do not: yell, spray water, cover the cage, etc...
I would recommend putting him in his cage, turning away, and then promptly turning back and praising him for being quiet. Start with immediate praise and treats, and work your way up to brief time intervals, and then slowly longer time intervals until he learns to be quiet in his cage. Stay in the room with him at first, and then work on being able to leave the room and still have him remain quiet. Take it slow, keep the praise high, and ignore him the moment he starts screaming. Turn your back on him or leave the room.
At the same time, work on making sure he has plenty of instructive and ambient attention. These two types of attention are vital in screaming birds. Cuddling attention is not the only type. Spend time with him making sure he knows how to play with all of his toys. Show him new toys, and teach him how to play with these. Teach him how to play catch. Walk around the house and try to teach him new words (`Gosh, look! An APPLE! Do you like APPLE? I sure like APPLE! How about we get you some APPLE?`). Get his mind working.
Once he`s good at playing with his toys and entertaining himself, ambient attention will be easier. Just spend time in the room with him as you fold the laundry, watch TV, read a book, etc. Remember to look up at him occassional and talk to him to include him in what you`re doing, so he knows you`re aware of his presence. `Having fun with that toy?` `Gosh that grape looks good!` just stupid, silly little comments so he feels included. If he thinks he`s ignored he`s much more likely to scream.
I said earlier `don`t cover the cage` but what I really meant was don`t cover the cage if he`s screaming. By approaching (even to cover him) you reward the behavior. If you know in advance you need an hour of quiet time (perhaps your favorite TV show is coming on, or you have some important work to do) you can pre-emptively cover the cage. This`ll help keep you from getting frustrated and angry which is best for BOTH of you, and your bird won`t much mind a little one hour nap. Try not to use this excessively, and don`t forget to uncover him, but you`ll need a break sometimes and that`s one way to take it.
Other advice includes...
Whispering and singing softly. If he starts screaming, turn away from him and start whispering to yourself. He may quiet down to hear. Reward him for getting quiet, and reward him effusively if he imitates you. Whispering should be a VERY acceptable way for him to get your attention, try to teach him that.
Low energy, soothing music may keep him calm and happy. Find music he likes and play it for him.
HIGH energy music can be a great time for creating a condoned `screaming time.` Cockatoos are noisey little buggers, nothing to do for it. He will scream sometimes. Play some rock music, bounce around, start screaming, and get him to join in! After 10 minutes of being rowdy little monsters together bring down the energy, put on some soothing music, and quite yourselves down. This can help your bird work off some steam and keep the worst of the screaming to a decent hour (say, 6 PM instead of 6AM)
I hope this is helpful. Just remember to ignore bad behavior, and reward good behavior. Train yourself to notice when he`s being quiet. It`s so easy to forget them when they aren`t making a fuss, so it may take a little work to train yourself to do that! But it`ll be a big help if you do.
Goodluck!