I tried flying a Buzzard to the airfield as Trevor but I couldn't figure out how to save it there, and ended up accidentally deleting it. Any suggestions?
Helipads are used to store purchased or stolen helicopters. In order to save a vehicle to a helipad, it must be landed on the helipad and left there for a short period of time. After it's been landed, it will be saved to that character's helipad. Each of the three main characters will have their own library of helicopters.
Unfortunaltey, this seems to be pretty buggy though. The only time you will consistenly have choices of helicopters to choose from at your helipad is if you purchase new ones the option to "choose" at the helipad by pressing "right" on the d-pad will show up and you can choose between the ones you purchased and the ones you stole and parked there before.
By default, Trevor has a helipad at his Sandy Shores hangar. He also has the most expensive purchasable helicopter in the game saved to this helipad.
Both Michael and Franklin can purchase helipads at Vespucci for $419,850 each.