How can you get a permit for flying a helicopter?
You need to get a flight physical, attend ground school, pass a ground-school test, attend flight school, then pass the FAA oral and practical exams. Flight instructors from the school close to my office (I work on the perimeter of a small airport) tell me it's about $10,000 LESS expensive to learn to fly an airplane before you start learning to fly the helicopter than it is to learn to fly a helicopter first. Check philip.greenspun.com 's section on learning to fly a helicopter; he goes into it very well.
You do not say which of the helicopter missions in GTA IV. But, if it is of any help: All of the helicopter missions on GTA IV are helped enormously by helicopter flying practice. It is worth jacking one of the Maverick helicopters from Helitours in Algonquin and practising taking off, flying, and landing, regularly, until you are able to do this easily. You can then approach the chopper missions with more "flying" expertise.