Turn off the power supply to your thermostat at the breaker. Remove your old thermostat by taking off the face plate and unscrewing the wall mount. Label each wire with a small piece of masking tape according to their connection on the old thermostat. For example, R for red and W for white. Pull the wires out 3 to 4 inches from the wall before you disconnect them from the old thermostat. Bend them down so they don't fall into the hole in the wall.
Detach the wall mount from the back of your Honeywell thermostat. Feed the wires through the hole in the wall plate and position the plate on the wall so it is level. Mark where the screws will go with a pencil. Remove the wall plate, being careful not to let the wires fall into the hole in the wall.
Drill a hole at each of your pencil marks. Feed the wires back through the face plate. Insert a molly anchor into each hole and then use the screwdriver to insert a screw into each molly anchor to mount the wall plate.
Connect the wires according to your labels. For example, the label for the R wire connects to the terminal on the back of the thermostat with the letter R next to it, and the W wire connects to the terminal with W next to it. To attach a wire to a terminal, unscrew the terminal one or two turns with the flat head screwdriver, wrap the wire around the base of the terminal and then tighten the terminal to secure the wire in place.
Insert three AA batteries into the back of your thermostat. Remove the red tab at the left hand side of the thermostat. Stuff the wires back in the wall as you slide the thermostat into position on the wall mount and snap it into place. Turn your circuit breaker on again. Program your thermostat with the time, date and your heating and cooling settings.