Instructions
Walk west on Route 42 or east on Route 38 to get to Ecruteak City. Go to the Burned Tower, located in the northwest part of the city.
Enter the Burned Tower and take the ladder on the right to the lower floor. Your rival appears to battle you with a Quilava, Magnemite, Gastly and Zubat. Defeat his team to move on.
Go down the next ladder to enter the Burned Tower basement. Walk down the stone stairs towards Entei, Raikou and Suicune. When they spot you, the three Pokemon run away. Leave the Burned Tower.
Walk around in any grassy field in Kanto. Entei and Raikou appear at random, so you do not know where to find them at first. Once you see them in battle, if they flee, their locations are marked on your map. Entei and Raikou have a high flee rate, so try to freeze them or put them to sleep before using an Ultra Ball to catch them.
Go to Cianwood City, located west of Route 41. Walk north until you see Suicune. When it sees you, Suicune flees to a different spot.
Head toward Mt. Mortar on Route 42. As you approach the entrance to the mountain, you see Suicune again. As before, it runs away.
Walk or fly to the Kanto region. Walk west on Route 11 to enter Vermillion City. Head to the port to find Suicune, who flees again.
Leave Vermillion City and head east on Route 11. Turn right on Route 12 and go south. Follow the path to reach Route 14. Suicune appears here and then leaves.
Go back to Route 12 and head north. Turn left on Route 9 to reach Cerulean City. Go north on Route 24 and turn right on Route 25. Suicune stands in front of a house on Route 25. Approach it to start a battle, then capture Suicune in the same manner as Raikou and Entei.