How to Get into the Dragon's Den in Pokemon Silver

Head to Mahogany Town via the map and defeat the gym leader, Pryce. He has three Ice-Water type Pokemon: Seel, Dewgong and Piloswine. Use Electric and Grass type moves to defeat them.

Talk with Professor Elm once you leave the gym. He will tell you that Team Rocket took over Goldenrod City Radio's tower. Go west to Goldenrod City to battle Team Rocket's Grunts and make your way to the top of the Radio Tower.

Talk to the Radio Director when you get to the tower and he tells you that he is really the Team Rocket Executive. You'll need to defeat him to obtain the Underground Key. He brings five Koffings and a Weezing with him to the battle. They can all be beat by using Psychic type attacks. After beating him, go back down to enter the Goldenrod Underground and go to the right. Use the key you received on the door in the Underground.

Enter the door and you'll find a puzzle that you need to solve. Move the switches so they read "three, two and one," going from left to right. Once the switches are set in the right positions, a new room will open up where you will face the true Radio Director. He gives you a Card Key that will open more of the doors in the Radio Tower. Make your way to the top of the Tower again and use the Card Key to go through the third floor door.

Advance to the fifth floor and face off against two Team Rocket Executives, a male and female pair. The female brings a Arbok, a Vileplume and a Murkrow to fight you. Use Psychic, Fire and Electric against each respectively. The male brings a Houndour, a Koffing and a Houndoom to the fight and you should use Fighting, Ground, Rock and Water moves against them.

Travel to Blackthorn City after defeating the Executives and fight Clair, the Gym Leader for that city. She has three Dragonairs and a Kingdra with her. Use Ice attacks and Dragon type Pokemon. Once you defeat her, she will let you in the Dragon's Den.