A room thermostat is the means of controlling your heating and air conditioning system. Low voltage (24 volt) wiring runs between the thermostat and the furnace. Typically there are several individual wires contained in a cable. Each of these wires controls a specific function (heating, air conditioning, fan, etc). While it may seem complicated to wire a thermostat to a furnace, it is a fairly straightforward process that an average homeowner with home improvement skills can accomplish.
Turn off the power to your furnace and thermostat. Either turn the switch off on the outside of the furnace cabinet or turn the breaker off in the circuit breaker panel.
String a thermostat cable from your furnace's control board to the location your thermostat will be. Use a fish tape to pull the wire through the wall. This will allow you to not have to remove drywall to install the wire. Leave 6 inches of excess wire near the thermostat and at the control board of the furnace.
Mount the wall plate for the thermostat. Pull the thermostat wire through the opening in the back of the wall plate. Level the wall plate on the wall and fasten it down.
Strip the outer cable back 2 inches to expose the individual wires. Strip each of the individual wires back to expose 1/4-inch of bare copper. Do this at both the furnace and the thermostat location.
Connect the wires to the control board of the furnace: red to "R" terminal, white to "W" terminal, "Y" to yellow terminal, black to "C" terminal and green to "G" terminal.
Connect the wires to the thermostat in the same fashion as you did to the furnace in the preceding step.
Snap the thermostat onto the wall plate and turn the power on to the furnace. The thermostat should now be fully functional.
Always make sure the power is off before wiring the thermostat. This will prevent damage to your furnace and/or thermostat.