Instructions
Complete enough individual missions to open the second island of Vice City. Since the game is rather open-ended, you can choose which missions to do at any given time but you'll be notified when the second island is open.
Drive to Escobar International Airport. The game comes with a map that will help you locate the airport and get to it.
Go to the left of the airport to the automobile entrance. From there, you can locate several planes on the runway. One them says "Plummet" on the side.
Drive up to the small biplane that is past the "Plummet" airplane. It has four wings.
Get out of your vehicle and enter the plane by pressing the "Triangle" button. You will now be able to fly the plane.