No electricity but have a Ford Econoline van with a 12v Auxiliary "Power Point" Outlet (and more)
You can get inverters that will connect to your vehicle's 12 volt battery, and produce "household-style" 120V AC.  Low-power inverters, up to about 200 watts, can plug into the "power point" or lighter outlet.  Higher power inverters must be wired more directly to the vehicle battery.

Beware when running an inverter from the vehicle battery that you don't run the battery down so far that you can't start the engine!!

Your APC UPS, if charged via an inverter or from "shore power" (home power outlet) could run your PC for an hour or two, depending on the actual power requirement of the PC.

Edit, to repond to the OP's questions...

Your APC UPS is intended to plug into a normal AC outlet, and will normally pass the AC power from that outlet to any loads you plug into it, while also charging its batteries - no additional batteries are required.

If you have no AC power avaialble, and need to run AC-powered equipment from your vehicle, you will need a 12 Volt DC -> 120V AC inverter to produce the required AC from you vehicle's battery.  I suggest that you add a separate "house" battery to prevent discharging your vehicle battery.  This house battery would be connected to the vehicle battery through a "battery combiner" so that it would be charged, along with the vehicle battery, when the engine is running, but disconnected from the vehicle battery when it is not.

You would then connect an inverter to the "house" battery to provide the AC that your computer requires.

Jumper cables should only be used for very temporary connections - if you are making a permanent installation, you should use proper large cables with suitable terminal lugs, bolted to the battery and inverter.

Small inverters, rated for 250 watts or less, my be plugged into a lighter outlet ("power point" now, since smoking is discouraged.)