It's one of the hardest things to do effectively, especially as a public official.
Sometimes it's best not to respond; you don't want to keep the story alive or give your critic more exposure. Sometimes the attack is undeserving of a response.
When you know you need to respond, striking the right tone is not easy. Too often, the response appears defensive. You need to take the criticism seriously, but not take yourself too seriously.
Here's an example of how Mayor Cory Booker, the Mayor of Newark, New Jersey, responded to a joke, a big put down of Newark, from late night talk show comedian Conan O'Brien. In my opinion, Mayor Booker's response strikes just the right balance of seriousness and humor. It's shot on a video format in just over 1 minute, making it the perfect length for both broadcast and YouTube dissemination. Now the country is laughing with Newark, not at Newark.