Instructions
Releasing and Locating the Legendary Dogs
Travel to Ecruteak City and go enter the Burned Tower, which is located on the northwest portion of the city. Your rival will challenge you to a Pokemon battle.
Defeat your rival and travel northwest until you reach a rock. Have one of your Pokemon use the HM Rock Smash to break it.
Continue east and then south until you reach a hole in the ground. Walk over the hole to fall down it. You will encounter the three legendary dogs, who will then retreat into the Johto wilderness.
Walk in the tall grass portions of the Johto region. You will randomly encounter one of the legendary dogs, although only very rarely.
Capturing The Legendary Dogs
Use your Pokemon to attack the legendary dog until its health meter is low.
Use an attack that puts the legendary dog to sleep or paralyzes it. Examples of these could be Butterfree's Sleep Powder attack or Pikachu's Thunder Wave attack.
Throw Ultra Balls at the legendary dog until it is captured. This may take several attempts as the legendary dogs can break free from Pokeballs more easily than other wild Pokemon can.