How to Get Lugia in Pokémon Silver

Obtain the first seven badges. To obtain the gym badges, you must defeat the gym leader for each badge.

Get the Silver Wing. You get it after defeating Team Rocket at the Goldenrod Tower.

Go to Whirlpool Islands. Use your town map to find it.

Go through the Whirlpool Islands. At this point, you'll need a Pokémon with Flash.

Find the elderly man at the end of the dungeon. Then, go down the stairs.

Lugia should be in the cavern below. Save your game so that you don't lose progress, and prepare for the battle.

Once you are ready, walk up to Lugia and press A to talk to it. It'll let out a battle cry, and you start the battle. Do not use your Master Ball.