you go to the ocean/sea (next or in between rout 14 & 15)then you'll see suicune. it'll then run up the water. then a man will come and challenge you to find suicune the fastest.
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You will need to chase Suicune to these locations after releasing it from the Burned Tower in Ecruteak City: north of Cianwood City; Route 42 (just outside of Mt. Mortar); Vermilion City, on the dock; Route 14 (east of Fuchsia City); lastly you will be able to battle and catch it on Route 25 after encountering it at the previous locations.
After route 14 he will go to his final location: Route 25. But! If you kill him in route 25, he will re-appear after you beat Red.
You will first see Suicune in the north of Cianwood City.Then you will find it next to the entrance of Mt. Mortar,then it will head to Vermillion City in Kanto,after that you will find it on route 14,and finally you will be able to capture it on the edge of route 25.
In Route 14 of Kanto
Suicune is in the burnt tower, but then it runs away and u will encounter it in various places. go to serebii.net or look it up on google then go to the heart gold soul silver link and look for legendary Pokemon there will be some stepsSuicune is seen in the following places and you must follow it if you wish to capture it. First, it will be found in the north of Cianwood City. After you encounter it there, you will shortly find it outside the entrance of Mt. Mortar in Route 42. Once you find it here, it will leave Johto and head to Kanto where you will see it in Vermillion City soon after you arrive. Next you will see it in Route 14 where it will escape for the final time to be found outside Bill's House in Route 25. This is where you battle Suicune.