Where exactly does the ground line go in an AC-DC power supply?
Two are "hot", and one is "ground".


This is incorrect. One is "hot". One is "neutral", and the third is safety ground.


  My question is: if I'm building the circuit shown, where do I solder the ground line? 


If the case is metallic, you should bond the ground wire to the case. This prevents the case becoming energized and electrocuting your users. (Because if the hot wire comes loose and contacts the case it will throw a breaker)

If your case is plastic and is "double-insulated" then no ground wire connection is required. 

Since the ground wire is usually only connected to the case, it isn't normally shown in schematics for the circuits inside the case.