Legendary and Special Pokemon
Latios and Latias

After defeating the Elite Four, you will be asked what color the new Pokemon that's flying around Hoenn is. Answer "red" for Latias, or "blue" for Latios.

The Eon will immediately be "let loose" - you can find it just about anywhere in Hoenn now. Since you haven't seen your respective Lati yet, I suggest you just wander around until you see it. Lati@s can be found on the water and in grass.

Once you find your Eon for the first time and you enter the battle, you should use False Swipe to bring its health down. After one turn, it'll run.

Now that Lati@s is in your Pokedex, you can check its area for where it
is at the moment. This is a real pain to do, so pay attention....

When you check your Pokedex, one route will be highlighted. Lati@s moves from one route to an adjoining, when you move to a different route or city. Basically, if Lati@s is in route 102 and you walk from Oldale to that route, your Eon will probably move to either route 101 or 103. It will never go into a city, so dont worry about that even though there may be grass/water there.

Every time you encounter Latias, you should try to inflict a Status Condition like Freeze, Sleep, or Paralyzed (not Burn or Poison because those inflictions will hurt the Pokemon and eventually faint it) and throw Ultra Balls at it. But if you can get another Master Ball, or haven't used yours yet, you won't have to endure the chase.

Once caught, Lati@s is level 40, and a Psychic/Dragon type.