I am going to totally pass over Giuliani's more recent checkered actions per the 20 year rule of this sub.

After 9/11, Giuliani functioned as the main spokesperson for New York City, and New York's Response was massive. Around 91,000 people total were involved in rescue, recovery, and cleanup. Giuliani did play a role, but the response New York had to 9/11 took a lot of different people doing a lot of different things.

For example, Jerrold Nadler, who represented the 8th district of New York, set up an emergency task force for the 34,000 residents of lower Manhattan, which worked to find shelter for people displaced from their homes and coordinated with pharmacies to send messengers to deliver prescriptions to people unable to travel, among other things. Ted Monette, who worked as the "man on the ground" for FEMA, had people going door to door checking houses and informing people of the various charities and services that were available. Most of the rescue and recovery coordination happened in a giant warehouse called Pier 92, which the government actually had bought months before for a bioterrorism drill scheduled for the 12th.

Giuliani held a meeting each morning with strategy advisors from all levels of government, and did daily tours of both Ground Zero as well as vising triage sites and hospitals. He also went to dozens and dozens of funerals. He coordinated multiple efforts across many different areas of the government as well as with charities such as the Red Cross, who ended up helping about 25,000 families. He also held multiple press conferences each day, where he repeatedly praised first responders and often gave solid information such as numbers of wounded and locations of blood drive centers. He was actually in 7 World Trade Center when the North Tower collapsed, and ended up trapped for about fifteen minutes.

He helped to set up the Lower Manhattan Development Corporation, which was tasked with rebuilding the area around the World Trade Center. Two members of the board have since claimed that $45 million of its funding was unaccounted for.

Giuliani's relationship with the aftermath of 9/11 is not all rosy. He was criticized for the slow response to the health effects of the attacks, as well as the fact that many first responders did not have proper safety gear - namely, respirators. He re-opened Wall Street only six days after the attack, against the recommendations of some officials. There are now 10,000 cases of cancer associated with 9/11, and more people have died from exposure to toxic particles than died in the initial attack.

It's been said part of the reason so many firefighters died is that they had faulty walkie-talkies, and did not hear the order to evacuate. Giuliani was criticized for not ensuring the departments had working equipment. The walkie talkies were known to be faulty since 1993, but the department had fallen back on them after their replacements turned out to also be faulty. They had simply not bothered to get around to re-replacing them yet. When confronted about the faulty walkie talkies, Giuliani claimed they were functioning, but that the firefighters chose to remain in the building to continue helping people. Further investigation suggested that only 24 of the 32 firefighter companies had at least one member who heard evacuation orders.

Source for a lot of this: "Catastrophe and the Public Service: A Case Study of the Government Response to the Destruction of the World Trade Center", Steven Cohen, William Eimicke and Jessica Horan, 2002.