Instructions
Play through the game until you encounter Latios. This Pokemon can be found anywhere, so use the PokeGear in different areas to see if Latios is around. He will show up on the PokeGear if he's near your location. You can also cast Repel to keep smaller Pokemon from attacking you. Repel doesn't work on Legengary Pokemon like Latios, so using it will increase the odds of his attacking you.
Use an attack that will prevent Latios from running away. You can use the Mean Look attack or the Wobuffet attack, as either one will keep Latios in the fight. Follow those attacks with any of your regular attack moves. Your goal is to get his health as low as possible without killing him.
Use the Ultra Ball on Latios once his health has been almost drained. The Ultra Ball is the most effective method available of catching enemy Pokemons.