The tantrum (in my opinion) was precipitated by something - whether a want or a demand - that is typically not rewarded. With my children, I would caution them ahead of time that if they "acted up" or didn't listen to Mommy, that we would leave the store.  I'd also reward them with something for being good - typically something like chocolate milk or cookies at home- nothing from take-away's or the store itself.  
Most times this was enough of a deterrent that we didn't have any worries.  Sometimes, I had to leave the store/restaurant - a) to avoid the embarrassment b) to diffuse the situation and c) to follow through with my warning.
Going to the store on their schedule was also a better plan- when they had been fully rested, fed and contented - not due for a nap, grumpy or hungry.
(and then, there's always the leave 'em at home if it's an option).
Just know that every parent feels your pain and they suffer right along with you when your child is in full public display having a meltdown.
Just wait until the teenaged years - when they defy you and embarass you in public in ways that make the two's look positively charming!
Good luck!

Welcome to the not-so-excusive club callled parenthood! hehe!
It's only with time and experience that you figure out all the things you could have/should have done...most of us old-timers just offer advice because we want you to avoid what we went through.
I too didn't have many issues with tantrums - and sometimes you can see in other parents that it's their short fuse and not the child - other times, for sure, it's a cranky todddler.
Oh the joys!
P.S.  This new topic is great!

give love and time to ur kids


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