You start off controlling the eponymous Sly Cooper on the rooftop of Police Headquarters. After the conversation between him and his pal, Bentley, you can explore the rooftop if you would prefer to learn the basic controls, and even smash a few antennas with Sly's caneto score a few coins. Otherwise, just focus on the main task here, which is getting up to the air vent. Head up the small ramp lined with coins to the ledge of the water tower. Here, you will be introduced to special blue sparkles known as stealth auras. These auras are going to be your friend, as they can be used to pull off sneaky moves, such as sneaking along ledges. Go towards the stealth auras and hold down to sneak around the ledge. Then use to jump across the two TV antennas to get to the air vent. Smash it by pressing , then head inside until you reach a ledge above a vertical shaft of yellow lasers below. You have to jump to the other ledges lining the shaft, avoiding the lasers. If you hit a laser, when you reach the bottom, you will have to smash the alarm siren to advance any further.
Smash the siren, and the door will open up, allowing you to traverse the halls. Carmelita's office is marked by the red door. Run through the corridor by turning left twice, and you'll find it. However, the door is blocked from the inside, so you must take an alternate route. To your right is a window with a ledge leading to the window of Carmelita's office. Remember to hold near the stealth auras to sneak along the ledge. Once you're at the window, jump in and feel free to smash up any objects in the room for more coins, or just go to the vault and press to enter the vault code, which is 9-3-7. You can use (or the directional buttons) to move Sly's hand left and right, as well as to turn the tumbler by pushing up and down; you can also use and to go left and right, and and to turn the tumblers up and down.
After taking the file, your last task here is to escape to the Cooper Van located at the end of the parking lot below. Once you regain control of Sly, run out the window onto the fire escape. Sly will then be confronted by Carmelita. While dodging Carmelita's pistol fire, run down the fire escape lined with coins and make a run for the van. The parking lot is littered with police cars and barriers. Do not jump over any of the police cars, as Carmelita will shoot them, causing them to burst into flames. It is better to run in between them, destroying any barriers in your way. Hop into the back of the van and you have escaped Inspector Fox!