Instructions
Start a new game. When it begins, walk downstairs and exit your house. Walk north to meet Professor Oak who will take you to his lab. After explaining a few things and meeting your rival, he will offer you one of his three young Pokemon. Select Charmander. If you select one of the other two, you will never find Suicune in Kanto.
Play through the entire story mode of the game. Collect all eight badges and defeat the Elite four to open up the post-game side quests, which includes searching for the legendary Pokemon, who now will roam the fields in Kanto.
Walk through the grassy areas in Kanto looking for Suicune. Search long enough and you will come across this Pokemon. Engage it in battle.
Throw the Master Ball at Suicune to capture it immediately. If you do not have a Master Ball, attack it with strong grass-type or electric-type Pokemon, since it is a water-type. Use a trapping attack to make sure it does not run away. Try not to kill it as there are no other Suicune's in Kanto to find.
Weaken Suicune so it will be easier to catch. Throw Ultra Balls and eventually one will catch Suicune and it will not escape. Take Suicune to a Pokemon Center and heal it so you can add it to your party.