Obtain the tail number for the plane whose flight is to be tracked. They are usually located, appropriately, on the tail of the aircraft. If it is not possible to see the aircraft, it can be determined by using one of several databases available online that can determine a tail number with some identifying information, such as departure airport and time of flight.
Access one of several free flight tracks available online, such as FlightAware or FlyteComm.
Type in the tail number into the relevant section of the tracker. For example, from the FlightAware homepage, there is a box on the sidebar where a user can input a tail number to bring up tracking information.
Click "Track Flight" to bring up the status of the private flight. It should also provide further information about the flight, such as duration and arrival and departure airports.