Ok,ok,ok I know that Latios is a pokemon that runs every time you see it..

Beat the Elite Four. Have you never been on this site?

To see latios, just walk around and do what you would do anyways, but make sure to always have a masterball or wynat/wobbufet of at least lv 50 and a stock of healing items and ultra balls with you. Then when you run into it, either use the masterball or switch to your wynat/wobbufet on your first turn and then carefully weaken it and throw balls (you can also throw balls before weakening it, but this doesn't work as well). This prevents a lengthy legendary hunt. If you have already seen it and let it escape, an easy way (relative to the others) is to go to 2 or 3 adjacent routes (118-119, 128-129-130, etcetera) and switch between them untill you two are in the same route. Then just search around in that route untill you find it and capture it using one of the aforementioned methods.

Okay, first you have to beat the elite four, but after that, you gotta get lucky. You will not have his data on the pokedex, so you will have to meet it in the wild. After you do, try to catch him. If you don't catch him the first time, thats all right. Look on your pokedex for his location, and if he's where you are, look for him in the same route youre in. If hes not in your route,change routes. each time you chang routes, it will change routes too.