Instructions
Find Suicune on top of the hill in the north of Cianwood City in the Johto region. It will run away as soon as you approach it.
Continue on through the game to the entrance to Mt. Mortar on Route 42. Here you will encounter Suicune again --- but, again, it will run away when you get near.
Complete the Johto region by defeating the Johto Pokemon League, and travel to the Kanto region. When you arrive in Vermillion City, you will spot Suicune, but once again it will run away.
Proceed through Kanto to Route 14, where Suicune will run away from you one final time.
Defeat Misty, the Cerulean City gym leader, and head to Bill's House on Route 25.
Encounter Suicune for the final time outside Bill's House. This time, it won't run away, and you will be able to battle it. It is a Level 40 Water-type Pokemon, so you should be able to beat it fairly easily with an Electric or Grass-type Pokemon.
Capture Suicune in a Poke Ball without knocking it out. If you do knock it out, you can encounter it again at the top of the Burnt Tower, but only after you've defeated the Kanto Pokemon League.