1. Just keep playing the game until you've seen him.
2. After seeing him, you can track him down with the Pokédex. Since he moves to a different route each time you do, it can be a bit tricky to be on the same route as him, but you'll learn with practice.
3. Carry a strong Pokémon with the move, False Swipe. (You can use a stronger attack, but you risk KO, in which case you must reset your game without saving.)
4. Track Suicune down and False Swipe him. Repeat this process until he's at 1HP.
5. Track him down and use a sleeping move such as Spore.
6. Save your game.
7. Take a Pokémon with the ability, Arena Trap, or Shadow Tag.
8. Track Suicune down with this Pokémon in your lead slot.
9. Begin throwing the Pokéballs of your choice.
10. If Suicune KOs your lead Pokémon or uses Roar, reset your game and try again. (It's VERY important that you NOT save if it uses Roar. If this happens, it disappears from your game forever.)