How to figure out how to wire a 2 wire furnace to 3 wire thermostat
Well, in the old wiring system, it doesn't really matter which wire goes to which terminal on the low voltage side of the transformer. Therefore, your installer didn't really care if they mixed up R and C on the transformer. 

Which, I think, is exactly what your installer did.  Note that the transformer has an R and C terminal labeled.  Assuming the red wire  goes to the thermostat, that belongs on R.  If the white wire goes to the furnace relays, it belongs on C.

It should be straightforward from there.