How And Where Do You Find Articuno, Moltres,and Zapdos Platinum Version?

You have to get the national dex, then go to pal park which is on route 221 talk to professor oak then you go talk to professor oak in Etrena City. Then motres, zapdos,and articuno will appear on your pokemon marking app on your poke tech. Hope that helped a little bit. :D

They are roaming sinnoh after you get your national dex. .

After you complete the sinnoh dex they will show up roaming sinnoh on your poke tech map.

Go to Professor Oak ar Eternal City AND talk to him and he is going to say that the legendary pokemon will appear in your poketch app wer you find mesprit

First of all you need to complete the sinnoh pokedex, then fly or go to Etrena City. Go to professor Oaks house ( it's beside the gym ) He'll say to you that 3 legendary birds are in sinnoh. Use your marking map on your poke watch. Get marking map from the place where the clown gives out the second coupon in jubilife city. ( you must defeat  I say 5 ) gyms. Then choose who you want to catch first ( it wont matter ) go to that location and it wil run away. Keep chasing it about 10 times and it will finally stop ( I know it's annoying ) last of all use either 'Block' or 'Mean look' so it can't escape then weaken it and throw tonnes of the kind of ball that you like. ( I say ultra balls ).