One way to stop a tantrum.
When my daughter is in the midst of a tantrum because I've told her no to something, I ususally just say to her, firmly and calmly, "Does having a tantrum change my answer?" My daughter typically stops her tantrum within a couple of seconds after I ask her that and says, "No". Then I say, "Let's talk." Then, she and I sit down and calmly discuss why I told her no and why she was having the tantrum (i.e. why was what she wanted so important to her that she had a tantrum when I told her no). She then understands why I told her no and I have a better insight into why my child responded the way she did.
Occasionally, when I learn more behind her motivation of what she wanted, I do change my answer, only after she and I have calmly discussed things. If I do change my answer, I explain to her how her calmly telling me more information about her desires gave me more information to make a positive answer (in preschool talk, of course!). She learns that she can calmly explain her viewpoint and change people's view through calm talk and negiotiation. She learns that mommy really does say no for a reason. She also learns that tantrums really don't solve a problem. I learn more about what makes my daughter unique!