Instructions
Wait until Monday night on any week, between 8 PM and 11:59 PM in real-world time. The game will run according to the time zone to which your Nintendo DS is set.
Go to Mt. Moon in the region of Northern Kanto, which is between Pewter City and Cerulean City. Fly to Pewter City and head west on Route 28. You'll have to fight some trainers along the way. Eventually, you'll reach a Pokemon training center. Look around this area for a small cave and enter it.
Go to the top of the mountain by fighting your way through the different levels inside the cave. You'll encounter a rival trainer just inside the cave, and you'll need to defeat him. When you exit the cave, you'll be at the top of Mt. Moon.
Wander around until you come to a small pool in the center of a square of cliffs. The moon is reflected in this pool. The Clefairies should be dancing around it. They will keep dancing until they see you, and then they'll run away, leaving behind the moon stone. To get it, simply pick it up.