What should I do if my preschooler wouldn't stop screaming because I didn't want to buy him a toy at the mall?

Once you give in, it's over. He'll then scream every single time he wants something, and you'll go broke. The reason why parents cave in frequently is because they are uncomfortable with the stares of passers-by. You have to be really thick skinned, and tell him that he can cry all he wants but he won't be getting anything because he cried for it. "What a pity. I'd wanted to buy it for you at first, but because you threw a tantrum, I've decided I won't buy it for you after all. Perhaps we could consider it the next time you behave at the mall." This will teach him that crying will not get him anything.