1.  Click Corrections and then Private Invoice. This actually brings up the Receipt screen, and in fact you can perform private invoice corrections while receipting. Type in the amount you want to correct for each service, and then press Correction. Give a basic reason for the correction. 

2.  From this screen you can also perform discount and bad debt corrections in the same manner, (press the Bad Debt or Discount button instead of Correction). They are all more or less the same thing, you are writing off all/part of a service that was billed for some reason.

See also: Refund a receipt or credit