How to test grounding in AC outlets?
There are two, somewhat related problems that can happen to the earthing system in a house

Your earthing system isn't connected to earth well enough (or at all)

This is mainly a problem due to lightning etc. inducing surges on the power line -- the earthing of your house's power grid limits these surges to a manageable value for other things (like surge suppressors).  Ed Beal's answer covers testing for this, although it's not a terribly high priority to fix.

Your earthing system isn't connected to the neutral/return well enough (or at all), or is connected improperly to the neutral/return

This is the main issue people complain about when they say their house has "no ground".  The bond between the neutral (return) and ground (earth) systems at the service entrance is what allows the ground system to serve as a safety mechanism against exposed metal parts becoming energized.  However, it can be defeated by being absent altogether, or by an improper cross-connection between earth and neutral.  There are two tests to perform here, in addition to a visual inspection of the neutral and earthing systems:


The energized yoke test -- this involves seeing if a non-contact voltage detector held near the normally earthed yoke of a receptacle is set off.  This test catches a very dangerous situation where the neutral and earth contacts on the receptacle are both inadvertently hot while the hot contact is connected to the neutral -- in North American practice, this is called a "reverse polarity bootleg ground".
The earth bond/ground loop impedance test -- a specialized tester called a "ground loop impedance tester" is used for this.  It plugs into a receptacle and measures the impedance it finds between ground and neutral -- this catches other issues like an open ground, or a "bootleg" connection between neutral and ground located at the receptacle.  If one is not available, a voltmeter measurement from neutral to ground with the circuit loaded can substitute -- this should read half a volt to a few volts on a properly wired and loaded circuit due to voltage drops in the loaded neutral wire, but will read nearly nothing if a bootleg ground is present at a receptacle.  Unfortunately, bootleg grounds may be present in other places in the electrical system as well, and are far harder to catch when they are, often requiring a lucky visual sighting of the errant wire to find.