Instructions
Go to the statue of the ancient god Arkvoodle. He will give you a task to complete. When you complete it, you will get a new landing point for your flying saucer on the map. (Whenever you complete a new task, he will award you another landing point.)
Go to the landing point when it is unlocked and stand in the center of it. Press the triangle button.
Wait for the flying saucer to appear. When it does, you can enter it and ride off.