Article: You're going to need a Level 40 Pokémon to take on Latios. Get a Trapinch or a Wobbuffet or any high level Pokémon that knows Mean Look (such as a Golbat or Crobat). Give a Pokémon that has Mean Look the Quick Claw ability and buy some Carbos for it (to be sure it's a top speed). Put this Pokémon at the top of your party. Wobbuffet and Trapinch are useful because their Shadow Tag (Wobbuffet) and Arena Trap (Trapinch) abilities will keep Latios from escaping. These will be your best bet for catching Latios. A regular Poke Ball is not recommended. If you chose Trapinch or Wobbuffet, whittle down his HP and throw tons of Ultra Balls. Otherwise, use Mean Look right at the beginning of the fight. If you make Latios faint, reset. If he gets away, you can now track him with your Pokedex, in the style you use to track the legendary dogs in G/S/C.
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Have your Pokémon ready. Buy tons of Ultra Balls. Use your abilities.