There are a number of companies around the world who conduct inflight calibration and flight checking of all ground based aids including radar and military installations.
The governing state determines how they want the aids to be flight checked and usually contract flight calibration units to conduct these flight checks.
Experience and training requirements are determined by the contracted company.
The aircraft usually carries a flight inspector who operates the on board equipment that assess the performance of the particular aid that is being flight checked.
As for flight crew it is not just a matter of flying the aircraft but also having a very good knowledge of the system both ground based and that contained in the aircraft.
I trust this explains the operation.