Before you touch anything, confirm the new thermostat matches your system. Check whether your equipment is heat only, cooling only, a heat pump, or a dual-fuel setup. The new unit's box and manual list the system types it supports. If the old base's wire letters are unclear, the data plate on the furnace or air handler and the outdoor unit usually tell you what you have.
Cut the power at the breaker that feeds the furnace or air handler, and set the old thermostat to off. Remove the cover. Many thermostats run on low voltage, but treat the whole job as a power-off job, because the equipment itself is still live at the breaker panel until you switch it off.
Label before you remove. Put a strip of tape on each wire and write the terminal letter that the old base shows it on. Take a photo of the old base with the wires in place. Keep the old base until the new unit runs correctly, because the photo and the base together are your reference.
Mount the new base level, pass the wires through the opening, and fasten it. Keep bare copper from touching any other terminal. Connect each wire to the matching letter on the new base. If your heat pump has an auxiliary or emergency heat terminal, check its label before you connect anything to it.
Restore the breaker and run a short test. Set the new unit to heat and wait for the blower and burner or heat pump to respond. Then switch to cooling and fan and confirm each one starts. If any mode fails to respond, cut the power again, check the wires against your photo, and stop if the match is still unclear.
If a wire does not match a clear letter, or the system needs a terminal your new unit lacks, call a licensed pro before going further. Once the test passes, set the schedule, file the manual with the equipment records, and note the swap in your file. For the planning side of your heating equipment, see the gas furnace service life and planning page.