After encountering them in the Burned Tower in Ecruteak City, the three Legendary Beasts – Raikou, Entei, and Suicune – will roam freely across the Johto region. Catching them is a significant side quest and a test of patience. Unlike Gold and Silver, Suicune has a more prominent role in Crystal's story and will appear in fixed locations before you can catch it.
Raikou and Entei: These two will randomly appear in any patch of tall grass on any route in Johto. They will flee after one turn, so you'll need a Pokémon with a move like Mean Look, Arena Trap, or Shadow Tag to prevent their escape. Using the Master Ball is also an option, but it's generally saved for other legendaries. Track their locations using your Pokégear's map, which updates when you enter a new area. Save frequently!
Suicune: Suicune will appear in specific locations throughout the story (Burned Tower, Cianwood City, Route 42, Vermilion City, Route 14) before finally settling at the Tin Tower (Bell Tower) in Ecruteak City, where you can battle and catch it. You'll need the Clear Bell to access the top of the Tin Tower. This makes Suicune much easier to track and catch than its counterparts.