Instructions
Defeat the Elite Four and save your game. After watching the game's ending credits, you will be returned to your home.
Check the TV in your house to watch a short program, which will trigger Latios to begin wandering the map.
Catch a Pokemon, such as Wynaut, Trapinch or Wobuffet, with the Shadow Tag ability. This ability prevents wild Pokemon from running away. Keep this Pokemon in the first place in your party while searching for Latios. Alternately, you could teach a Pokemon like Gengar or Sableye the move Mean Look, which serves the same purpose. The only concern with using Mean Look is that if your Pokemon is too slow, Latios may run away before you can stop it.
Stock up on Pokeballs, especially Ultra Balls, which have a high capture rate. Always have at least 20 to 30 on hand in case you encounter Latios unexpectedly. If you have the Master Ball, you can skip this step.
Wander the map, heading into tall grass and surfing on dark blue water whenever possible. The first time you see Latios is the most important, since seeing it will add it to your Pokedex and make it easier to track if it manages to run the first time.
Use the Master Ball to instantly capture Latios.
Lower Latios' HP into the red if you do not have the Master Ball, but be careful not to knock it out. If you can, use a move like Hypnosis or Sleep Powder to put Latios to sleep, as this status makes catching wild Pokemon easier.
Throw Pokeballs until you manage to capture Latios.
Check your Pokedex if Latios escapes, since the Pokedex will show Latios' location. If Latios is nearby, walk to the route mentioned in the Pokedex and head into the tall grass, where Latios should eventually appear. Repeat steps 7 and 8 as necessary until you catch Latios without it running away.