It's really important not to give in to bad behavior. Put them in a spot and walk away. If they get up, go back and put them there again, and walk away. Temper tantrums should not be rewarded with attention.

I agree with explaining things to kids. I know a lot of people who don't believe in doing that, that it's coddling, but I disagree, as long as you wait until they've calmed down and you haven't reinforced their bad behavior. I think explaining things helps kids learn to control their emotions, because understanding things means they can't say to themselves, "There's no reason I can't [fill in the blank]! Mommy and Daddy are just mean!" when they understand the reason.