Hi Kelly....
You should watch SuperNanny. I swear that's my response to soooo many moms on here, but she's so good. She teaches a lot of basics that I think Moms should focus on b/c it makes life so much easier. One of them is that you don't give in, regardless of the child's behavior - but it's all about how you do it. She typically advises for parents to set up a "Naughty chair" or corner or something in a place that isn't related to fun (i.e. a toy room or their bedroom, but some place more like the dining room or a hallway or something) and that's the place they need to go when they misbehave. She helps parents to set up the structure of discipline that helps parents stick through it and follow thru while avoiding the stress of it all (well, pretty much anyway), but also teaches kids discipline in a way that isn't threatening or in turn teaching the child bad habits. I really recommend that show.
Personally, I don't put up with the screaming temper tantrums and my 7 year old daughter knows it. She's only had 2 in her life and each time (once when she was a toddler in a supermarket and once just a few weeks ago in fact) I dealt with them differently because of her age. But the thing is that regardless of how I discplined, she has known her whole life that Mom doesn't put up with that. I was honestly shocked when she did it a few weeks ago because it's completely out of character for her, but I had to stand back and realize there were a few factors involved (she was overtired). Maybe those outside factors are a reason why your son does it.
Another thing I've read is that with kids, it's typically all about getting attention. They aren't able to differentiate between good attention and bad attention, they just want attention. See, your son is young enough that you can teach him now that behavior like this won't get him what he wants - which means that no matter what he is screaming for, BY NO MEANS DO YOU GIVE IT TO HIM WHEN HE ACTS LIKE THAT or you teach him that that is how he gets his way and he'll keep doing it. Trust me on that one.
Okay, I've been rambling for a while now. You should go on that website and see info about the show. I think you can even watch full episodes online. Give it a shot. She's sooo good!!
Hope this helps. Take care (and grab some ear plugs!!).
R. :)