Well I start with a time out. Tell him that the more he cries or screams the longer he'll sit there. Even if he has to sit the for 20 min sometimes. Then I get down to his level make him look RIGHT AT ME, and talk to him about why he's doing it and why he shouldn't be. It took awhile for me, but my son is almost 5 now and he's alot better now. Don't get me worng, he still has his days like any other kid.
ignore it! Easier said then done, I know, but I have 3 kids, the youngest is 3 as well, so I know whereof I speak lol...it is mostly about manipulation and control. Make sure fatigue and hunger or sickness are not the issue. Sometimes they melt-down when they are tired, or over stimulated. But mostly it's a way to get their own way and you can NOT give in, even once, becuase if you do, that sends the message that a temper tantrum will get them what they want. I can NOT stress this enough...do not give in to the temper tantrum! As well, you should know it is totally normal and all 3 year olds do this...who says the 2's are terrible? In my experience it's always been the terrible 3's...Good luck!