Instructions
Choose the starter Pokemon Charmander after heading to Professor Oak's lab at the beginning of the game. Picking Charmander allows you to capture Suicune later in the game; choosing the other starters -- Bulbasaur and Squirtle -- lets you capture Entei and Raikou, respectively. Progress through the game until you defeat the Elite Four, opening the opportunity to search for Suicune in the Kanto region.
Teach your Pokemon moves that prevent Suicune from fleeing battle. Moves such as Mean Look and Block, and physical moves like Bind, stop Pokemon from fleeing. Status effecting moves such as Hypnosis make Pokemon fall asleep during battle, while moves like Flamethrower and Toxic inflict burn and poison status effects that deplete a Pokemon's health. Level your Pokemon to about level 50; use grass and electric Pokemon to have a slight advantage against Suicune.
Use your Pokedex to search for Suicune throughout the entire Kanto region. You can encounter Suicune on any route; its location changes each time you exit a building or travel between routes. Walk around in grass or use the HM, or Hidden Move, Surf to traverse any body of water to encounter Suicune.
Battle Suicune after encountering the Pokemon using a Pokemon with a type advantage. Utilize moves that may prevent Suicune from fleeing battle. Weaken Suicune until its health reaches the yellow or red range. Trainers can use any kind of Pokeball to capture it, including a Master Ball, which immediately captures any Pokemon at the start of battle.