Instructions
Enter the Highwind by pressing "Triangle" when Cloud is standing next to it on the overworld map.
Fly east of the Chocobo ranch. You will see an island chain in the eastern portion of the map with a cave at the northern tip.
Turn the Highwind south and fly until you see an island with a grassy area on the right and a rocky flat portion separated by a small cliff. Line the Highwind up with the very edge of the cliff using the "Square" button and the directional pad.
Move the airship over the cliff and press "X" to land. As you land, hold "Square" and move forward and to the left. Cloud exits the airship from the front, so you should be able to walk on the flat rocky portion of the island where the Highwind can't land normally.
Walk northward along the island until you reach the cave. This cave contains the Quadra Magic Materia.
Walk southward to the base of the cliff and press "Triangle" to enter the Highwind again.