This circuit uses the popular and easy to find LM3914 IC. This IC is very simple to drive, needs no voltage regulators (it has a built in voltage regulator) and can be powered from almost every source.
This circuit is very easy to explain:
When the test button is pressed, the Car battery voltage is feed into a high impedance voltage divider. His purpose is to divide 12V to 1,25V (or lower values to lower values). This solution is better than letting the internal voltage regulator set the 12V sample voltage to be feed into the internal voltage divider simply because it cannot regulate 12V when the voltage drops lower (linear regulators only step down). Simply wiring with no adjust, the regulator provides stable 1,25V which is fed into the precision internal resistor cascade to generate sample voltages for the internal comparators. Anyway the default setting let you to measure voltages between 8 and 12V but you can measure even from 0V to 12V setting the offset trimmer to 0 (but i think that under 9 volt your car would not start). There is a smoothing capacitor (4700uF 16V) it is used to adsorb EMF noise produced from the ignition coil if you are measuring the battery during the engine working. Diesel engines would not need it, but i'm not sure. If you like more a point graph rather than a bar graph simply disconnect pin 9 on the IC (MODE) from power. The calculations are simple (default)
For the first comparator the voltage is : 0,833 V corresponding to 8 V
* * * * * voltage is : 0,875 V corresponding to 8,4 V
for the last comparator the voltage is : 1,25 V corresponding to 12 V
Have fun, learn and don't let you car battery discharge... ;-)