Instructions
Proceed through the game until you reach the West Dust Hills. You encounter a scientist who tells you Dr. Holiday kidnapped his daughter. Once he's done talking, you're free to explore the area.
Walk north -- the only road available -- until you come across a woman blocking your path. She tells you that Dr. Holiday is actually a good guy. Once she's said her piece, she leaves, allowing you to continue down the road.
Continue down the path, until your way is blocked by yet another girl. Do not talk to her. Instead, take the small path to the east. You'll find a man there.
Speak with the man, who gives you the gemstone. You don't even have to pay or fight for it.