Instructions
Unlock Cresselia
Complete the main story quest and receive the National Dex.
Travel to Canalave City, which is found at the end of Route 218.
Enter the house in the southwest corner of the city. Speak with the boy and his family. They'll send you looking for Cresselia's Lunar Wing, which will cure the boy of his nightmares.
Exit the house and speak with the father. He'll take you to Fullmoon Island via a boat.
Travel up the stairs and down the path to the right. You'll encounter Cresselia, but you cannot capture her yet. She leaves the Lunar Wing for you to take. Grab the Lunar Wing. Return to the boat and speak with the father. He'll take you back to Canalave City.
Enter the boy's house and give him the Lunar Wing. He'll be cured. From now on, Cresselia roams the wilds. You can find her in outdoor maps throughout Sinnoh.
Capture Cresselia
Place a Wobbuffet at the front of your party. It must be between level 31 and 49, and it must have the skill Shadow Tag. You can get Wobbuffets in the Three Lakes maps.
Go to a Pokemart and purchase repel. You can find a Pokemart in any city.
Travel to Route 210. It's between Celestic Town, Solaceon Town and Route 215.
Walk to Route 215 and then return to Route 210. Keep walking between the two until the Poketech Map reports that the Cresselia is in your current location. Apply repel and wander around the map until you initiate a random battle. So long as your lead Pokemon is between level 31 and 49, Cresselia is the only Pokemon you will encounter.
Attack Cresselia until her health meter is red or yellow. Throw pokeballs until you capture her. Typically, she tries to run, but so long as you have a Wobbuffet with Shadow Tag at the front of the party, Cresselia won't be able to flee.