The connection or coupling from the power plant to the Alternator depends on the required Voltage and amperage the Alternator will put out at a given RPM.
If the Alternator will put out the required power at the standard running RPM of your power plant a direct "Love Joy" type of coupling will work well just make sure it is rated for the torque/Hp load. If the RPM of the power plant is not high enough most APU's will use a poly v drive belt with a increasing speed ratio.
I have used both and either works well but alignement is key!
On Chinook helicopters the APU (turbine) drives a hydraulic pump that pressurizes the utility hydraulic system. The utility hyd system drives an AGB(aux gear box) that contains alternators, flight hydraulic pumps, etc. Once the main engines are up to speed the APU engine is shut down and the AGB is driven from the rotor system after gearbox.
Also the utility hydraulic system is used to start the APU turbine so a handpump for the utility system is provided in case the system needs charging. It had a tendency to leak down overnight, but still an ingenious system that allowed us to be pretty autonomous in remote areas.