Grand Theft Auto 5 offers a wide variety of activities, but the most common activity is the stealing of cars. As luck would have it, that's not the only thing you can steal. In fact, you can steal a jumbo jet and fly around Los Santos at will.
Before you can steal a jet, you first have to find one. The best place to do that is the airport. Take a look at your map and head down to flight training if you have that option available. If not, just make your way to the airport in the lower left corner of the map.