Turn off power to your home heating and air conditioning system by turning off the correct circuit breaker in the circuit breaker panel.
Remove the old thermostat from the wall and disconnect the wiring. The wires are usually held on by screws. Label all wires as you remove them so they can be reconnected to the correct terminals on the dial thermostat.
Unscrew the wall plate from the wall and remove it. Install the new wall plate with drywall anchors and screws.
Check the thermostat wires to ensure they are stripped sufficiently. There should be 1/4 inch of bare copper exposed on each wire. If there isn't, strip them with your wire stripper.
Connect each wire to the new thermostat. A typical configuration of a dial thermostat has the red wire connecting to the "R" terminal, the white wire connecting to the "W" terminal, the green wire connecting to the "G" terminal, and the yellow wire connecting to the "Y" terminal.
Push the thermostat on to the wall plate until it snaps into place. Turn the power back on to the heating and air conditioning system.
Set the dial on the thermostat to the temperature you prefer. The heating and air conditioning system will maintain that temperature.