How do I use three-prong appliances when my outlets are mostly two-prong?
I'm assuming you're in the US.

Get a tester and see if the box is grounded. A two lead neon type tester works well for this. Insert one lead into one side of the two-prong outlet and touch the other lead to the screw that holds the plate on. Try the other side, too. You may have to scratch off some paint if the screw isn't bare metal. If it lights up that's good news. You can use a multi-meter set to read AC voltage or another type of tester instead of the neon one.

If you have grounded boxes, you can either buy two-prong to three prong adapters that have a lug that you put the plate's screw through or you can buy replacement outlets that are designed for retrofitting in this application.

Your other option is to have an electrician come in and upgrade your wiring to full grounding.