Push a thumbtack or pin into the wall in an inconspicuous spot to test its hardness. Drywall is softer and won't crack. Plaster is much harder. A plaster wall won't want to take the pin and will probably splinter.
Find an area in the home where you can see behind the walls or ceilings, perhaps an attic or basement. If you see lath and plaster pushing through, you know you have a plaster wall.
Remove a switch plate and look at the electrical wiring. If the wiring is loose and you can see lath, your walls are plaster. If the wiring is enclosed by an electric box, your walls are most likely drywall.