Instructions
Go to the Pokemon League, located past Victory Road, and beat the Elite Four. You wake up in your bed at home.
Head downstairs to talk to your mother. She takes you to the television to hear a news report about a strange Pokemon sighting. At the prompt, answer either "Red" or "Blue" to determine the color of the Pokemon. If you answer "Red," the Pokemon will be Latias. Answer "Blue" if you want Latios.
Walk around anywhere in the Hoenn region where wild Pokemon appear, like caves and grassy patches. At random, Latios or Latias appears to fight you. The Pokemon runs away immediately without giving you any chance to catch it.
Look at your map. Now that you have seen Latios or Latias, its position is tracked on the map. You must walk to the marked location. If you fly, the Pokemon moves to a different location.
Search the grass where the Pokemon's location is marked. Use a Repel to ward off all weaker Pokemon in the grass, if desired. At random, Latios or Latias appears.
Throw your Master Ball at Latios or Latias to capture it instantly. If you don't have a Master Ball, use a move like "Mean Look," which prevents a Pokemon from fleeing. Then attack it to lower its health, and throw Ultra Balls at the Pokemon until it is captured.