Get a small voltage tester. All it needs to have is two wires and a little light. They sell them at any hardware store.

Go find one of your three prong outlets. Look at the two slots. If the ground pin is at the bottom, the left slot (taller than the right) is the neutral, should have a white wire. The shorter slot on the right is hot.

Try your tester by putting one of the probes in the neutral and one in the hot. It should light up.

Now put one in the ground pin hole and the other in hot. If its grounded, the tester will light. If it does not, that ground is not connected to anything.

Word of caution: some jackasses will connect the neutral to the ground on the back of the outlet. This is stupid and dangerous, but it will pass a quick test like the one we did. You should take at least one of the three prong outlets apart and check. If they did it once, they probably did it many times.

Turn off the power to that outlet (use your new tester to verify that the power is off) and pull the outlet apart. You might get lucky and find that the wiring had a ground wire (bare copper wire) that was just tucked away. You can just get a proper grounded outlet and attach the bare wire to the green screw.

Before you pop the bubbly if you find that bare copper wire, you need to test it again. With the outlet pulled out (leave wires connected to original outlet) probe the hot (black) wire and touch the bare copper ground wire. The tester should light up. If it does not, the copper ground wire is not connected to the ground in the breaker box (or in some older homes, the ground wire is connected to copper plumbing).

If the ground does not work, you can go on a hunt to find out why. Most houses, one outlet will daisy chain to another. If an upstream outlet has ground wires, but were not connected, that will be a problem. You can work your way backward to see if you can find and connect them all. If you're taking the outlets apart, you may as well expect to do this anyway.

If the ground was tied to plumbing and someone replaced a copper section with a nonmetallic (pex, PVC) the ground will no longer work.

I would advise to at least try to figure out what is going on. You'll learn a lot in the process and as a homeowner, its really important to understand your electrical system. Open a few outlets and probe (carefully). If you hit the wall, you may need to get an electrician in. They can probably tell you what's up and then you can do the gruntwork of rewiring outlets.

Setting up a ground system isn't that hard, it involves bury a few rods and do some wiring. I did it for my house, but I had an electrician expert tell me what to do and how yo do it properly.

Said so, get ground wires absolutely and a ground "stuff" (not native English speaker don't know the correct word).