After a brief bit of Googling, I discovered that I couldn't find anything on the internet about replacing the CMOS (or BIOS) battery in my Asus F3JC laptop, just spam pages responding to the keywords with a useless page. So here's the information in a nutshell:
It uses a CR2032 coin battery (you can buy them from your local shops for a dollar or two), the location is between the two RAM slots and the main battery, and under the main back panel cover. See the photo, below, I've sat a battery directly above the spot.
It's not directly accessible without more disassembly than shown in the photo. But it is possible to swap the battery without removing the entire bottom panel, and it probably takes less effort. I did contemplate removing the entire bottom cover, but after removing all visible screws it was still firmly attached in place.
WARNING: Do not hold a new charged battery cell in a metal tool that will short the top and bottom surfaces of the battery together. If you must use tweezers or pliers to hold the battery, cover at least one end of them with non-conductive sticky tape.
Unscrew and remove the larger hatch cover. Reach in under the plastic with a small screwdriver, flip the battery out of the holder. Slide in the new battery, angle the far end down into the battery holder contacts, push the near end down firmly (use a screwdriver to lever the battery against the plastic back of the laptop). Its positive side faces the outside world.
Boot up your laptop and follow the prompts to press F2 to get into setup and set your clock to the right time (and any other BIOS settings that you want to customise).
If you don't feel confident in doing any part of this yourself, find someone else to do it for you. Don't mess up your computer. Be aware that your computer may not be identical to mine.
WARNING: Newer batteries are worse at leaking than older ones (due to chemistry changes in manufacturing over the years). When you get a flat battery, remove is as soon as reasonably possible.
For enquiring minds: What is the CMOS or BIOS?
The BIOS (Basic Input Output System) is a small amount of code written into firmware in a computer for booting up the system, and provides very basic access to the hardware. Once the system has booted, it ignores most of this, and your operating system takes over. But it also has some configuration information that may continue to be in effect on a fully running system, hence why its usually important to replace a flat battery.
CMOS (Complementary Metal Oxide Semiconductor) is the type of low power electronics that the BIOS circuitry typically uses, or at least the parts of it that kept the clock going and stored the BIOS settings. Though there's no reason why another kind of electronic device could be used.
Modern computers use UEFI (Unified Extensible Firmware Interface) instead of BIOS. It's doing the same jobs, but it's an updated system with (potentially) more features.