How are fan and compressor discs balanced?
This article covers the issue (and is a pretty interesting read) but does not really explain how they do it. It just says 


  After machine balancing, the part can then be manipulated (mass added
  or removed) and retested on the machine until satisfactory balance
  tolerance is achieved.


In answer to this question,


  And what method do they use to determine where the balance point is?


The device is pretty similar to that of a tire balance, here is a video of one in use and here is an interesting sales brochure for one.