1. Silver Wing: This item is given to you by the elder of the Whirl Islands after you complete the "Lugia's Curse" sidequest. This involves finding and speaking to all the elders on the Whirl Islands.
2. Rainbow Wing: This item is found on a hidden island near the Whirl Islands. The island can only be accessed by using the "Dive" HM, and the Rainbow Wing is hidden in a cave on the island.
Once you have both items, you can go to the Whirl Islands' central chamber where Lugia will be waiting for you.