You have to realize that tantrums are the result of frustration. Your little girl is beginning to see all the wonderful things that are possible in the world, and yet she either isn't coordinated enough to be able to do them, can't verbally express her desire to do them, or the big people in her life are not letting her! (And sometimes for very good reason! =)
The way I dealt with tantrums with my two daughters was this. When the tantrum began (or even a full-on snit that preceded a tantrum), I'd say, "I can see that you're mad that Mommy won't let you put your crayons in the dryer." Then very calmly I'd walk the child to her room and sit her down and tell her, "When you're feeling better, you can come out." And then I'd leave the room to let her sort through it. Of course, sometimes the child would be full-on screaming, thrashing on the floor, and if that was the case, I'd pick her up as carefully as possible and carry her to her room.
My kids always knew that this was a cooling-off period, a chance for them to collect themselves, vent their frustrations, whatever needed to happen, and NOT a punishment. To this day (they are now 5 and 8) I will still send them to their rooms until they're "feeling better" when they give me any kind of attitude. It's a good coping mechanism for a child to know that they can go to their own space, take a few minutes to be as mad as they want to be, and then re-group and join civilized society.
I would employ this same tactic if a tantrum happened in the grocery store or Target or wherever. We'd just leave the cart, go out to the parking lot, and the offending child would sit in the back of the SUV until they "felt better." Of course I'd get some funny looks from people as they walked by the car and heard my howling banshee of a child in the back of the car, as I'm standing outside the car watching... but it worked for us.
If your child has a meltdown while standing in line at the DMV or pharmacy... let her. Chances are everyone else will get so sick of hearing it that they'll let you to the front of the line. LOL