Instructions
Speak to the Radio Director in the Radio Tower of Goldenrod City, and he will give you the Clear Bell. Enter the Burned Tower, which is north of Ecruteak City. Descend the ladders and stairs in Burned Tower to get to the basement. In the basement, the Legendary Dogs will scatter around Kanto.
Train a Ground-type Pokemon and an Electric-type Pokemon to Level 40. Teach the two Pokemon Ground-type moves and Electric-type moves. Raikou and Entei are weak against Ground-type moves. Suicune is weak against Electric-type moves. Unless you plan on using Master Balls, buy 50 to 100 Ultra Balls.
Look for Suicune, Entei and Raikou in the routes of Kanto. They will randomly fly to different locations. Once you encounter a Legendary Dog, use a Master Ball to catch it. If you don't want to use a Master Ball, weaken it with Ground-type or Electric-type moves. Once the Legendary Dog has one hitpoint, catch it with an Ultra Ball.
Go to the Pokemon Center in Celadon City. Talk to Eusine, who is standing before the counter, and he will tell you about a rumor of a rainbow-colored Pokemon. Leave the Pokemon Center and go to Ecruteak City. Enter the long building that has a man standing a few steps before the entrance.
Descend the stairs and exit the building. Follow the path and enter Tin Tower. Speak to the man who is standing between two elders. The Wise Trio member will give you the Rainbow Wing. Stairs will appear next to you. Descend the two sets of stairs.
Pick up all the Item Balls and continue descending the stairs. You will need to jump over ledges to find the stairs. Use the pink tiles to teleport to different parts of the Tin Tower. Save your game. Once you descend the last staircase, you will see Ho-oh. Go up to it and press "A" to engage it in battle.
Make the Legendary Pokemon easier to catch by decreasing its hitpoints. You can do this by using Ice-type moves on Ho-oh. Once it has less than 10 hitpoints, try to catch it with an Ultra Ball. If you choose to capture Ho-oh with a Master Ball, you do not need to weaken it. Restart "Pokemon Crystal" if you fail to capture Ho-oh the first time.