Know the triggers. Hunger, boredom, overstimulation, or exhaustion can send kids into fight mode. So figure out what sets your child off. If 30 minutes of shopping makes him grumpy, for instance, don't push him to go longer.
Calm him down. Grab your child's hands as he strikes and firmly say "No." Say that hitting isn't okay, but it's all right to feel angry. When he does, he should say, "I'm mad" instead.
Set a good example. If you flip out when your husband leaves his clothes on the floor, your toddler will probably flip out for similar small offenses. And when your kid acts out in public, don't let it cause you to behave like a toddler!