It is very difficult to deal with a screaming bird but the problem can be dealt with if you have the right amount of patience and knowledge. First of all, if your bird hasn't been examined by an experience avian vet recently, it would be best to start there. There are many potential physical causes for screaming and these should be ruled out first (also, a good avian vet may have more advice on curbing the screaming if it is totally behavioral).
The next thing I would do would be to try to determine if there is something that seems to set off the screaming. If it's a dog barking, try to work with the dog's behavior around the bird. If it's a doorbell, try "desensitizing" the bird to the sound by distracting him during the sound of the bell (ring it purposely to work on this) and offer him a favorite treat while the bell is ringing so that he learns to focus on other things while it's happening. Most of the time, people find that the cause of their bird's screaming is the owner themselves. Usually, the bird simply wants their favorite "flock member's" attention. The most important factor in curbing screaming is routine. It is going to be extremely important that you introduce some sort of routine into the bird's life. Birds scream for attention. If they know they are going to get interaction regularly (even if it's not a great deal of time) they are amazingly more well adjusted and less likely to act out by screaming. When your bird screams, he is saying "hey, mom, look over here... pet me, play with me, feed me treats [(smile)] ". If he knows he is going to get your attention daily at a set time, he will be less likely to be screaming for it when he sees or hears you .
You don't have to set aside a huge amount of time, just regulate the time you currently spend with him or add a block of time in the am and pm. Even 15 minutes will work wonders when it is regulated and kept up. Try to think about how much time you currently spend with him. Add all of the times he wins you over by screaming, the times you give him treats, the time you spend bathing him, feeding him, etc. Then, try to set times for these interactions to take place. You don't have to be extremely strict, just do your best. If you could spend 15 minutes of "one on one" time (time when you can scratch his head, talk to him and focus on him only) in the morning, that would even be good. Then, try to work it out to have him maybe share dinner with you or a shower. Even his "out-time" should be regulated so that it happens roughly the same time daily if possible.
Do not allow him in/out access on his own from his cage. You should be the one taking him out and putting him back and, when you do, try to regulate that time so that he gets to look forward to it. Try to figure out for you what is realistic for you to continue, and start a routine. If he is friendly to other family members, it will make it easier to keep up with the routine, because if you become busy, the other family member can keep up with his routine. This routine will take a while to produce results, but it will produce results. In the meantime, you want to refrain from reacting to the screaming if possible, covering him, yelling at him, spraying him with water or physically reprimanding him in any way. All of these things will produce exactly what you don't want... a neurotic, nervous and probably louder bird. If you come home and your bird is screaming his head off, wait for a quiet moment before you go to greet him. Try not to reward the screaming behavior by approaching him during that time. It is important to realize that he wants love and your time. You need to figure out a way to provide him with the love and attention he needs without giving in to his demands. The best way to do this is to provide the love and attention on your terms and with routine.
If you want to try the covering up the cage trick, only cover it for a five minute period, if it hasn't produced results in that amount of time, it won't and will quickly become abusive. If he does quiet down in the 5 minute time span, uncover him and give him a treat for his quietness. This will work much better than keeping him covered for extended periods of time. Also, while you are working on the routine, refrain from reacting to his screaming. If you have to remove him from the room, do so but do it quietly and business like. Once he is in the other room, listen for 5 minutes and (if you can) place him back in his regular space, praise him and give him a treat if he is quiet. If he isn't quiet, it isn't going to work and you should replace him in his regular room quietly and without acknowledgment. Spraying him with water will not only potentially cause a neurotic bird, it will also turn what should be a pleasurable activity (bathing) into a punishment. By screaming at him, you will most likely excite him and could cause him to become louder the more excited he becomes. Obviously, it is never, ever recommended to physically reprimand a bird. It is very easy to injure them with even the smallest of physical reprimands and it will only succeed in causing the bird to become afraid of you and potentially human hands in general---this is never conducive to training.
Also, in the meantime, try getting him some new, mind teasing toys. "Shredders" are a great toy for cockatiels and can be found at most pet stores which sells bird items. Also, toys made out of wood, suede and leather are favorites among tiels. You can try offering him a mirror as long as it doesn't seem to interfere with his tameness when you do. If he becomes nasty around his own reflection, you may need to remove or regulate the use of the mirror. The most important thing to remember is that behavior problems don't start overnight and usually aren't resolved that quickly, either. Patience and persistence are very important. For some birds and owners, getting a bird companion may be the answer.