To steal a police helicopter you must first steal a sport class car only.
You must then run over a pedestrian and stay put. If the police are called stand outside the car, kill police officers until your wanted level is high enough to get a helicopter is pursuing you.
You must then place an proximity I.E.D on the car. Then get in and out of the car almost instantly.
The blast should throw you into the air without killing you and giving you the brief opportunity to get in the helicopter with an onscreen prompt.