Connect an Hour meter

The ground would go to any good ground source. Does it have a key switch or on button? If so it would go to the switched side, and the hour meter will run anytime that wire is energized.

If you don't have a key switch you can also hook it to the output from the alternator, but if you do that you should install a 12v zener diode in parallel with it so it doesn't run fast when the alternator is putting out more than 12v.

If your generator has an auxilliary external 12v plug for battery charging etc., you could hard wire it to the back of the plug. That would be a 12v regulated source.

You can also consider one of these wireless hour meters.

I agree with Bob's suggestion, being that if it has a 12V output, use that.

If not, you could consider going to your local Radio Shack and getting a 12V 'wall wart' that will plug into one of the outlets and provide 12V DC for your meter. That way, there would be 12V and the meter would run whenever the generator runs.

As for the 12V Zener thing, well, you'd best know what your doing or you'll let out the 'factory installed smoke' in short order. The generator is really an alternator, it provides AC. About 340V peak to peak. You need a transformer to step it down, followed by conversion to DC (diode or diode bridge). It probably doesn't need to be regulated for the meter. A cheap wall wart power supply does all that for you.