Well, for one thing, Giuliani turned to professor James Q. Wilson's "broken window theory": that one broken window in a building only invites more windows to be broken.
Taking a cue from that, Giuliani got the police department to go after low-level "street nuisance" crimes and misdemeanors that were destroying life in the city. The prime example is the "squeegee men" who would descend upon drivers at intersections, try to wash your car windows, demand payment for doing so, and get belligerent if you refused. Also panhandlers, etc.
By taking steps to restore civil order at the lowest levels, the public perception began to change, to turn to almost being optimistic about the city's future.
He was also able to initiate police procedures that improved the cops' ability to put a dent in serious crimes, as well.
I've never been a lover of the big cities, New York City in particular. I have worked there regularly since 1979, in and out of Manhattan and also for a number of years in the Oak Point/Hunts Point area of the South Bronx. So I'm not a New Yorker per se. But I have seen the changes that the Giuliani administration wrought there, and they were amazing.
Who could ever have thought that the city of the Dinkins era - a crumbling, hopeless, "ungovernable" place - could enjoy a new Rennaissance?
- John
But, the crime rate was dropping from 1990 to 1993 while Dinkins was still mayor.