You'd run into it similar to any other shiny legend. Save in front of it at Dragonspiral tower, confront it, and if its not shiny turn it off and try again. Keep doing it until you encounter it as a shiny. There is no guaranteed way to run into a Shiny Reshiram, since its like rocket science to run into one at dragonspiral tower (requiring a full party and pc to get it there). Or you could hack one into your game with an action replay. Thats all I know, now stop bothering me about it.
I got it from someone who got it from someone else that he didn't know. Shiny Reshiram/Zekrom can be cought if you can get them to appear in Dragonspiral tower.