Get the Member's Card Key Item and go to the inn in Canalave City. You will then have a sequence where your character goes into the bed and falls asleep. You will then Appear on Fullmoon Island where Darkrai resides, and after either catching or defeating Darkrai, you then wake up. The Member's Card is an event-only item by the way and was distributed a little while back on Wi-Fi connection.
If u have AR and can find a walk through walls code just go to fullmoon island and walk to the right