It's been awhile, but I believe it is a voltage to frequency converter.
Take a 0 to 2 volt range. At 2 volts assume a count of 2000 per period of time. The meter will take the frequency from the VF converter and apply it to a counter. At the end of the time period that count will clocked to a register and displayed on the display. The counter will be reset to 0 and the cycle will start over again.
The voltage will be scaled to 0 to 2 volts before being applied to the voltage to frequency converter. This can be done as simply as using a voltage divider network of resistors and a switch. So if you go to a 0 to 20 volt range the voltage is divided by 10 before being switched to the VF. The decimal point is scaled accordingly on the display.
Current is measured as voltage across a precision resitor.