
The flights are relatively cheap for one simple reason - they were heading home empty after dropping the jet owners at their destinations. Aircraft owners are therefore happy to fill these "empty leg" flights even at greatly reduced prices to atleast recover the cost of flying if not make profit.
And you will be very surprised to learn that in some rare cases, these private flights can cost less than flying on commercial airlines. That's because the cost covers all the seats of the private jet so if you are flying with the whole family, the cost per passenger seat may turn out be much less.
The process of booking a charter flight is more or less the same as Expedia or Orbitz - the only difference being that each flight costs in excess of few thousand dollars and it's not guaranteed that you will find a private jet on your route.
OneSky Jets [Sources: International Herald, Fortune]