How do I tell if a ground is really grounded?

Inside your electrical boxes, do you have a ground wire that is part of the building wiring? If the wiring is "romex" cable you would have a black, a white, and a bare ground in each cable entering the box. If it is wired using conduit, the conduit may be the ground.
What else can you tell use about your house. How old is it? Do you have circuit breakers or fuses?

If the house was built in '85, everything should be grounded. If you want to be sure, use a multimeter set to measure AC voltage. With the power on (be careful), there should be about 120 volts between hot and ground. Or, with the power off and the multimeter set to measure resistance, there should be close to zero ohms between ground and neutral.

Not foolproof but here are two steps.

1. Using wires with alligator clips on the ends or other similar means connect a fixture with 200 watts of incandescent light between the hot wire and the ground. The lights should come on with full brightness.

2. Inspect your main breaker panel to see that all the ground wires in the various cables are attached to a terminal strip that in turn makes metal to metal contact with the panel frame (box; can) and there is a fat ground wire from the main panel to a ground rod or to the cold water pipe where the latter enters the house.