T.,
My kids are younger than yours, but we deal with tantrums from time to time :)
Something we have been talking about in my ECFE class is to set rules, with appropriate consequences for breaking them, talk about them with your child, and then STICK TO THEM.
Tell her what you think the appropriate discipline for a public tantrum is (no TV for 2 days, loosing a favorite toy, whatever works for you) and then make it happen. No going back. Also, I think what Beth wrote about actually just picking up and leaving the store is good too. You may have to make a self sacrifice of time and go back to the store by yourself later... change your dinner plans, what ever you need to do, but she needs to understand that there are consistent consequences for her actions.
Saying no is a very important part of parenting. Our ECFE class has also been discussing a book by a local author David Walsh, "NO: Why Kids--of All Ages--Need to Hear It and Ways Parents Can Say It ". I have ordered it from Amazon, but haven't read the whole thing... but it seems like a great resource. You may find it helpful too.
Good luck!
J.
SAHM to Charlie (3-24-05) and Joey (12-4-06)