Basic pruning advice
 

I've got a Paph. rothschildianum X Paph. glaucophyllum, also know as Paph. Vanguard 1921. Where should I cut the stem after the blooms have faded? Thanks.

Assuming this is not a multifloral or sequential bloomer, cut the old spike as close to its origin as possible. In time this portion of the plant will die back and new growth will begin at its base. If you see any new flower buds, leave the spike alone.