There is a "Fixed cup" and an "Adjustable cup". The fixed cup is usually on the chainring side.
The fixed cup is coated with threadlock and spannered in so it wont move any further.
True, there should be a shoulder.
Apply grease with a grease gun and slot the balls in one-by-one with a greasy finger.
The axle goes in and then the adjustable cup, pre-loaded with lots of grease and the balls.
Then the "Lock Ring".
Now the tricky bit. Holding the adjustable cup, tighten the lock ring to fix the cup in place.
It should be noted here that when the Lock Ring is tightened, it pulls the cup outward ( slack ) slightly within the thread hysteresis, so thread the cup in tight to let the lockring pull it to the correct adjustment.
It may take several attempts.
Re-adjust after a few hours riding.
If you are buying a new BB set, buy one with a Spanner fit adjustable cup, not one with the four small holes.
If your bike is not going to be entered in a Concours show, fit a cartridge (fit and forget) bracket.