Turn off your heating and cooling system completely using the main power switch. Once you are sure the system is powered down completely, you are ready to proceed.
Use the screwdriver to loosen the wire terminals on the back of the Weathertron thermostat. Remove the wires one at a time, labeling each one with the wire labeling stickers that were supplied with your Honeywell RTH6350D. When you remove the "G" wire from the Weathertron thermostat, label it with the "G" sticker Honeywell supplied, and repeat the procedure with all the wires you remove.
Connect each wire you disconnected from the Weathertron thermostat to the corresponding terminal on the Honeywell RTH6350D. Each terminal on the Honeywell is labeled prominently with a letter, so attach the G wire to the G terminal and so on for all the wires you removed from the Weathertron. Once all the wires are connected, power the heating and cooling system back on and test the Honeywell RTH6350D to make sure you wired it properly.