Releasing Suicune
Go to the Burned Tower in "HeartGold," located north of Ecruteak City. The Burned Tower is also referred to in-game and in other Pokemon literature as the "Brass Tower" or "Burnt Tower." Venture into the basement of the Burned Tower. You will be informed that the three legendary dog Pokemon -- Suicune, Raikou and Entei -- have escaped from the Burned Tower's basement. You will not be able to capture Suicune until it is released from the Burned Tower.
First Locations
Go north of Cianwood City, which is located in the Johto Region. Cianwood City rests to the west of Route 41. This is the first location where you will see Suicune. Next, travel to Mt. Mortar. Mt. Mortar is located to the north of Route 42 in the Johto region. Suicune will flee again and move onto its next location.
Second Locations
Head to the Kanto region, as Suicune has fled from the Johto region. The Kanto region is to the east of the Johto region. Go to Vermilion City, located to the south of Saffron City and just west of Route 11. You will see Suicune here before it travels to Route 14, located south of Vermilion City and east of the Seafoam Islands.
Final Location and Capture
Travel to Route 25. If you have not already been to the Cerulean City gym, you will find the Cerulean City gym leader Misty on this route near Bill's house. Speak to her to get her to return to her gym. Suicune will now appear outside of Bill's House. You will now enter into battle with Suicune. Weaken Suicune and use a Master or Ultra Ball to capture it.
Second Final Location
If you do not capture or defeat Suicune outside of Bill's House along Route 25, it will be located inside the Burned Tower again after you defeat the Elite Four at Indigo Plateau.