Remove the old thermostat face, but do not disconnect the wires. Attach a small piece of tape to the end of each wire, then write on the tape the letter of the terminal to which the wire is connected. Generally, these are letters like "R" or combinations of letters like "Rh" and "Rc." The wires are typically color coded, but older installation may not conform to the color standards, so marking each wire is the best option.
Tape the bundle of wires to the wall or a pencil so they don't fall back into the hole. Prepare the wall plate for connecting the wires by loosening the terminal screws. If the ends of the HVAC wires are bent, straighten them, as the Honeywell terminals use a socket-style connection.
Match the letters on your wires to the letters on the terminals of the wall plate. If you have two wires with "R" labels, remove the jumper between the "Rc" and "R" terminals; "Rh" or "R" is connected to the "R" terminal. Only connect "Rc" to its terminal if the jumper is removed. Once the bare metal of the wire is in the terminal socket, tighten the screw to secure the wire in place.
Match your wires to the function on the HVAC system if you don't have labels from your old wall plate. The "R" and "Rc" are 24-volt alternating current power from the heat and cooling systems. The heat really goes to terminal "W," and if you have a second stage relay, it goes to "W2." Connect the compressor contact to "Y" and, if you have one, the second stage compressor contact to "Y2." Connect the fan relay to terminal "G" and the common wire for the power to terminal "C." If you have a heat pump, use terminal "O/B" for the changeover valve, "Aux" for the auxiliary heat relay, "E" for the emergency heat relay and "L" for the emergency heat output.