In order to get Lugia, you need to talk to someone at Pewter City, and you'll get a silver wing when you do. You can encounter Lugia when you take the silver wing to Whirl Islands B2F.
In order to get Ho-Oh, you need to capture Raikou, Entei, and Suicune in your game (traded ones don't count). After that, you need to talk to a sage at the Tin Tower, take the rainbow wing from him, and encounter Ho-Oh at the top of the tower.
source (to prove that I didn't just wing the answer)