Outlet tester shows "open ground" on GFCI outlet
You are correct, GFCI receptacles can be used to replace old 2-prong receptacles when there's no grounding conductor.   If your home is old enough, you might assume that there is no ground at the receptacle.  However, if you want to know for sure, you'll have to inspect the wiring inside the box.  

A properly functioning GFCI receptacle, can provide ground-fault protection without a grounding conductor.  So as long as you're not plugging in high-end audio/video equipment (or anything that requires surge protection), you're probably okay.

As @Harper mentions. Press the Test button on the GFCI, and make sure it trips and resets properly.  Repeat this test every month, as these are likely not GFCIs that self test.