Instructions
Take the "Enigma Stone" to the museum in Pewter City to trigger the Latios event.
Capture any Pokemon under level 35 that knows "Mean Look." The easiest Pokemon to capture with this skill are Gastly or Haunter.
Capture any high-level Pokemon that knows "False Swipe." "False Swipe" will deal damage to the opposing Pokemon, but will always leave it with at least 1 HP or hit point. If Latios drops to 0 HP, it will faint and you will be unable to capture it. Cubone, Scyther, and Gallade can all learn "False Swipe."
Travel to where Latios is on the map. As Latios is a roaming legendary, his location constantly changes.
Attach the "Quick Claw" item to your "Mean Look" Pokemon and put it at the front of your party.
Use a "Repel" and walk into the grass. Roam around until you encounter Latios.
Use "Mean Look" with your first Pokemon immediately when the battle starts so Latios doesn't run away.
Switch your "Mean Look" Pokemon with your "False Swipe" Pokemon. Use "False Swipe" until Latios' health can no longer drop. Use any Pokeball to capture it.