The goal of a police officer is rather simple. Get a police car, helicopter or bike and arrest the criminals. When someone commits a crime, you'll get a message on your screen with the description of the crime and where it happened. Press "Y" on your keyboard to open the police computer while the car/bike is not moving.
To get a police vehicle you should navigate to one of the three police departments using /gps -> City -> Police department
In order to arrest players: Go near the people which are marked red on the mini map, go out of the car and press Left ALT key to arrest them. You will receive payout every time you arrest someone.