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.

There is no connection to earth ground here, and one is not needed. In fact this is typically an advantage of using a transformer like this--it isolates your circuit from what may be a noisey ground.

You can connect the earth pin to the chassis if you want. That will help with noise pickup, if the chassis is metal. In the event the live wires come loose somehow and touch the case, it's also a nice safety feature: the voltage will be shunted to ground. If you're using plastic casing, you can just leave the earth wire disconnected.