Just like at home, kids throw tantrums in public when they don't get their way. Let's say you take your child to the supermarket and he feels he absolutely must have a candy bar. When you say "no", there is a clash of wills that can result in a tantrum. Many public places, such as stores and amusement parks, are overwhelming for children because there are so many things they want but can't have. At home, you can walk away and say, "I'll come back and play with you when you give me your nice voice. If you want to scream, you can go outside." But in public, if your child's volcano erupts, you can't just ignore it because his behavior is disturbing other people.
In a soft voice say, "I know you're upset, but it's time to calm down". Stay in control because if she picks up that her tantrum is getting to you, and it probably is because you're concerned about what other people are thinking, she'll scream even more. Your anxiety reinforces hers. If she doesn't calm down, take her to the car. If she won't walk, carry her. Once there, hold her, look her in the eyes and say, "I know you are out of control. I am in control and am here to help you. I understand you are really upset because you want that candy bar (or whatever else prompted the tantrum), but here are the reasons why you can't have it. We can talk about it more once you calm down. But until you do, we are going to sit here." Eventually, he will get bored sitting there and quiet down.
Even though it seems easier to just give the kid the candy bar and get out of the store, everyone's looking at you, and you're wondering, "What did I do wrong? Mine is the only child out of control." However, your child has to learn that tantrums are not a means to an end, otherwise, he'll pitch a fit the next time you're in a similar situation.
Don't think other people are judging you. Nowadays, with lots of parents on the go with their kids, people are more accepting of public tantrums because they've been there, and if you can remain firm and calm in the face of a tantrum, I think people appreciate it. Yes, a few people may stare, but usually no one will say anything. Just focus on your child, and tune out everyone else. In fact, other shoppers appreciate parents taking a firm stand with their children. One time after saying "no" to our five-year-old, Lauren who wanted a candy bar at the checkout counter, the clerk said to me: "I wish more parents would say "no" to their children."
Parents should also keep a tantrum trigger list – what is it that tends to trigger tantrums in our child – and keep this in mind before you plan an activity.