Most large standby systems have a "request power" relay contact (closing the circuit actuates the relay that tells the controller power is needed from the load). The purpose of the auto start is to set the run-stop control to "run" and attempt starting until power is observed on the output. You should be able to modify (very lightly) ANY electric start generator with an electric fuel cutoff solenoid with an auto-start system.
What's basically entailed is that your OFF-RUN-START switch can be replaced with an AUTO-OFF-RUN-START switch, AUTO setting powers the auto-start controller, which watches the request power contact. When the request power contact is closed, the auto start controller energizes a relay that powers the original RUN circuitry, and then energizes a relay that powers the START circuitry until it observes power at the output at nearly the right frequency (50/60Hz) - then de-energizes the START relay. On better controllers, it can try to start a few times then give up to save the starter motor and your batteries, and the low oil, high water temperature, and low fuel alarm circuits will cause a shutdown automatically (by de-energizing the RUN relay).
When the request power contacts open, the RUN relay is de-energized and the generator stops running, on turbo-equipped generators, they can be set to run a no-load cool-down cycle.
For fixed installation generators they also feature a weekly exercise mode, where the generator run under no load (or under a load bank) to get up to temperature and stir the fuel, then shuts down.
The actual request for power would come from a load transfer switch, that detects the loss of GRID power service tripping the relay that requests power. When the load transfer switch sees power is available on the GENERATOR input, it closes an interlocked switch to power the loads from the generator. When the GRID comes back up, two things could happen: 1) on cheap/dumb transfer-switches+auto-starts, the interlocked switch for the GENERATOR source will OPEN, then the interlocked switch for the GRID will close powering the loads from the grid; 2) on more expensive/intelligent transfer-switches+auto-starts, the generator will match its frequency to the grid, then the GRID switch will close so the load is powered from BOTH the GRID and GENERATOR, then the GENERATOR switch will open (no load drop between steps).
For things like lightbulbs, or other items on a UPS system, the cheap/dumb kind of transfer switch and auto-start is fine. For industrial plants with high horsepower motors or very high electrical loads (think hospital), transferring the load all at once from 100% to 0% to 100% would probably blow fuses/breakers and melt critical power transmission components... here the cost of a frequency matching backup power system is easily justified.
Pretty simple stuff really.
