The Floyd Rose system is like any other bridge. It needs to be positioned at the end of the scale length (the distance from the nut to the bridge - it determines where all the frets are placed). That is a pretty basic piece of knowledge, might I suggest before you start, get hold of a copy of Make Your Own Electric Guitar, by Melvin Hiscock, it's a great book and will cover every question like this you have.
As for fitting a Floyd to a Les Paul/PRS, if you want to do it, that's cool - if you go ahead with it, might I suggest doing the routes before you carve the top - to give your router something stable to move across, instead of trying to balance it on the carve?