I've seen other preschool teachers simply say, “No thank you. We're not doing that.” Or “All done.” That doesn't work for me though.
When my daughter was two she really liked grapes. She called them berries. She was sitting in the shopping cart picking grapes out of the package and eating them. I told her if she didn't stop I would put them back. She didn't, so I did and I've never seen such a tantrum in my life! I had to take her out of the cart because she was wreathing around like a possessed person and I was afraid the cart would tip over on her- all the while screaming BERRRRRRRRRIEEEEEEEEEEES! I stayed calm and completely ignored her, even though I was well aware that everyone in the store was staring at us. She grabbed my leg and hugged it to try to keep me from leaving the grapes but I kept walking with her hanging on to me. When she saw that wasn't working she laid on the floor and clung to the shopping cart. The store manager came out and asked me what the problem was. I explained that she wanted grapes. He offered me free grapes. I said “I'm trying to teach her that she CAN'T get whatever she wants by having a tantrum.” Looking back, I probably should have taken her outside till she calmed down. But we both survived and she is not spoiled at all.