I have a 2 year old, too - And, I agree with Michele S's suggestion and sounds much like how my cousin disciplines her children (they are so well behaved)but, it didn't work so well with my sister's 3 1/2 year old - when he was 2 he was actually frightening sometimes. So basically, I personally think discipline may work differently for each child.
In my case, my son was a preemie and a little delayed in the speech area, and couldn't tell us why he was mad. And he started throwing the tantrums before he was 2 as well. And, after making sure that his basic needs were met (was he tired, was he hungry?) he simply was still very cranky. So, when the throwing (and hitting) started, we figured we had to do something so that he really understands that it is wrong and to preserve our sanity when he did it in public. We started the 1-2-3 method (There is a book called 1-2-3 Magic suggested by our occupational therapist). We read it thoroughly and followed the basic rules of no talking, no emotion. Basically, you count firmly but not angrily (because any type of emotional reaction to a tantrum is what they want) "That's 1" and give him 5 seconds to stop the tantrum, if he doesn't move on to "That's 2" again, give him 5 seconds, and at 3 he is sent to time out, for 2 minutes (1 minute for every year of his age). For serious offenses like hitting, we don't even count and we don't get upset, we simply put him into time out. For us (and I'm not making promises that it will work for everyone) it worked amazingly. Yes, in the beginning it was frustrating and we felt like we were putting him in timeout every 15 minutes, but, within about a week and a half, we would only get to 2 and he would stop the kicking and screaming. He would pout, but, he knew that he should stop. NOW, he stops at 1 and is actually starting show signs of understanding of being good and being bad. Which I'm sure all of this is part of the growing process, but it's nice that my son is no longer screaming his head off in the middle of the store. :)
As for time out, there are a couple of rules to that, too - they say you should designate a chair or a spot that has nothing fun or interesting near for him to entertain him...
Anyway, I wish you luck and I'm sure that you'll find the method that works the best for you. And Michele is right - it will pass (my sister's kid is an angel now at 3.5 and she had no method when all else failed)....