A heating-only thermostat is the easiest thermostat to install. It only uses two wires, usually red and white. The red wire is the power wire and the white wire is the heating wire. When the thermostat calls for heat, contacts in the thermostat close the connection between the red and white wires. This energizes power to the furnace and allows it to turn on and heat your home. When the temperature is satisfied, the contacts open and the furnace turns off.
Make sure the power to the furnace is off. Switch the breaker to the "Off" position.
Take the thermostat wall plate and mount it to the wall. Use drywall anchors and screws to hold it tight to the wall. Check it with a level and make adjustments as necessary to ensure it is level.
Strip the ends of the red and white wires back 1/4 inch with a wire stripper. Connect the red wire to the "R" terminal and the white wire to the "W" terminal.
Push the thermostat onto the wall plate until it snaps into place.
Remove the access panel from the furnace and look for the thermostat wire. It should connect to a terminal strip on the control board. Check to see that the red wire is on the "R" terminal and the white wire is on the "W" terminal. If not, make these changes.
Put the access panel back on the furnace and turn the power back on. Set your thermostat to your desired setting.