its tricky because you can't use block or mean look to stop it fleeing (it runs before you can make a move) the only way to catch it is to gets its hp down every time you see it and throw a poke ball until it is caught...
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you can get him by taking the s.s aqua to vermillion city then you will see suicune run from you when you docking to vermillion city then go west then steven the hoenn champion will tell you latios is running around on your pokegear map then you will see latios`s head all over kanto region running away from you its just like Entei, Suicune,and raikou did I HOPE I HELPED
When you get out of the Pokemon Fan Club after receiving the Poke Doll from the guy in there, Steven (from Pokemon emerald)will come to you and say Latios has escaped from Hoenn and came to Kanto.He will show you a picture of Latios, which will get updated to your pokedex.After Steven leaves, check the map in your pokegear.You should see a symbol of Latios somewhere in the map.That's where Latios is.Latios can escape from you easily.When you're close to the route he's in, he could move to a different place.At battle, Latios can run away at the first chance. Hope this helps!:)
Latios is still capable of running away even while a Trapinch with its Arena Trap is in the battle because Latios' ability is Levitate which allows it to avoid the effects of Arena Trap since Levitate Pokémon and Flying-type Pokémon cannot be blocked from escaping via the Arena Trap ability.
In Pokemon ruby you can catch latios but not latias, in Pokemon sapphire you can catch latias not latios, in emerald you can choose. Use your master balls on them so they wont fly away. You can use other types of balls, eg timer ball, ultra ball, or great ball on the other legendaries.
use mean look for not leting them run away, ghost Pokemon could learn it