Hi K.!
There is hope! =) I have a 6 year old daughter, and we have been through this also. The problem that arises in a tantrum is, they hope to make you so angry you give in and two they are struggling to find an effective way to show you how they feel, and due to the maturity level and the common "want what I want, when I want it" attitude leads to a tantrum.
I have found it most effective to first put a stop to the tantrum, sit down with my daughter and ask her "How does it make you feel when you act this way?" Does it make you feel good or happy? Usually the answer is NO! =) Then ask her if she rather feel upset and unhappy or if she rather feel happy? Usually the answer is "I want to feel happy" Explain to her that not only is she behaving in a way that makes her feel icky she is also pushing what she wants AWAY from her.
Explain that sometimes Mommys say no, but we have a reason why we have said no. Allow her to explain her self... Most of us parents are so programmed to respond with the timeless "BECAUSE I SAID SO" In my opinion as long as we are able to explain why we said no, on their level then why not just do it? The child feels validated and important when we do simple things such as take a few moments to explain. Dont get me wrong, it takes practice and you have to keep up with this, you cant try it a few times and expect it to stick but when you are repetitive with it, I promise you will see improvement, and in the mean time you will be shaping the manner that your child will interact with others. Kids continue this sort of behavior as I said before not only because they figure you will cave but also they have a need to be heard. The best way to completely put a stop to this behavior is to teach her how to talk to you and express her feelings with out being explosive. When she does something one way, simply explain to her how she could have done that differently, and explain to her what the likely consequences would be under each scenario. It is also a great idea to have this sort of talk with her when she is calm, and there is no current conflict at hand. Sit her down and let her know you would like to talk to her for a minute... If she is like mine she will fidget, and look around and play with whatever is next to her... Just gently ask her to pay attention when you notice that she is not, affirm the fact that what you would like to talk to her about is important... Have a talk with her before you go out also.. and just talk to her and let her talk to you. Encourage that she spill her feelings out to you, and when she finds it hard to articulate her feelings... Use your intuition, your a mommy you have one I promise! Ask her, is is that you feel this way? Why do you want this? Communication is the key!
Kids are people too, we as adults just have to remember that.