How do they do it
Reasonable question ... repeated.
Private and corporate operators are able to train either using their own aircraft and hiring or contracting specially trained instructor pilots, however most will contract time on a simulator for their type of aircraft. There are several providers of this service and the biggest is probably FlightSafety.
For service and maintenance they can contract with factory owned or supported service centers or with independant service centers that are either factory approved or just approved by the appropriate aviation authority for the registration of the aircraft. Example jetaviation.com
Some will hire technical staff at home base for minor flight line type support activity...but this is not essential for all aircraft.
Owning a private jet has many similariites with owning a car. If so;ewhat more dominated by regulations and complexity. Hence most owners will hire or contract professionals to manage the crewing and maintenance aspects of their aircraft. Those who don't generally deserve all they get.