I've been wondering about this for a while.  You guys don't know when an aircraft reaches Top of Descent...how do you decide when it's time to begin an aircraft's descent so s/he makes it down to the airport smoothly?

simple math...
 

From FL330

 

33 x 3 = 99... decend 99 miles away from the airport ( based on 1800fpm)

 

@ FL330, you want to be at 3000 at the IAF..

 

So 33000 - minus final alt ( 3000) = 30000

 

30 x 3 = 90..decent 90 miles from airport.

 

 

This is by no means a way of doing it on your theory test but hey, it works!

Usually, pilot report he is ready for descend. If it's necessary ATC might tell to pilot to expect to pass some waypoint at/above/below some altitude, so he can plan ahead. Of course, controllers monitor situation too, they can initiate descend at any moment.  
 
 
 

simple math...

 33 x 3 = 99... decend 99 miles away from the airport ( based on 1800fpm)

 
It's not. 
 
It's based on 1000ft of descend every 3 miles. So it's ground speed dependent. 1800fpm is for 324kt. But, if you take average ground speed at vertical profile for whole descend, you can easily come to number close enough to 324kt, so it works.

I know that math:  Didn't know controllers (real or otherwise) used it.

 

3*(altitude change in thousands)=miles to start descent

5*ground speed= descent rate

Not a controller (Vatsim or RL) myself, but I'd imagine it's also partially experience. Most planes will have roughly the same descent performance, so you need to start them down at roughly the same distance from the airport. I've also quite often received instructions of the form: 'initiate descent at your discretion, FL XXX by ABCDE'.