Cut the power to the furnace at the circuit breaker.
Raise the cover on newer wall thermostat models. On older models, the cover detaches and pulls off with gentle pressure.
Remove the screws holding the thermostat mounting plate to the wall. Pull gently on the thermostat and turn it around to inspect the back panel.
Label each wire connected to the back of the thermostat with a short piece of masking tape. Each terminal on the thermostat is labeled with a letter. Write that letter on the masking tape to label the corresponding wire.
Loosen the coupling screws on the thermostat to pull off each labeled wire. You can now remove the old thermostat and replace it with a new unit.