To get Latios, you must beat the Elite Four. After you beat them, go to your house and watch the TV, which says that there is a giant Pokemon flying over Hoenn. Your mum will ask you what colour the Pokemon was. Select blue. Now you can catch Latios. You can find it in any grassy area or any body of water, but not in caves. After you've seen him once, you can check his location on your Pokedex. However, every time that you change routes or go into a building, he moves, so you have two options:
1. Wait around for Latios and just go on with other things. You will run into him sometimes.
2. Find a route with a building and go in and out of the building, checking your Pokedex every time you come out to see if he's there.
Latios is extremely hard to catch, and I still haven't caught him, so here are some tips. Latios runs away on his first move, so either try to catch him straight away, or try to put him to sleep or freeze him on your first move. This gives you numerous shots at catching him, so it's easier. Remember, don't blast him with a powerful move and kill him. Once he's dead, he won't come back.