A transistor will vary its resistance in response to a voltage. The existing circuits input mostlikely has a pullup or pulldown resistor in which combined with the unknown resistance form a voltage divider to an ADC converter. Merely place a transistors collector and emitter leads on the input. Then apply your voltage to the base using the emitter as a common. You will need to bias the base to place it in the linear region and you will need a potentiometer to act as a voltage divider to allow you to adjust the input voltage aplied to the base.
http://www.eskimo.com/~ddf/Theory/Transistors.html
EDIT:
http://www.vellemanusa.com/downloads/0/illustrated/illustrated_assembly_manual_k8055_uk_rev3.pdf
I just looked at the schematic and instruction manual. The analog input is designed for a 0 to 5 volt signal and not a rsistance. The instructions on Pg18 state that the internal 5V supply can be used to simulate an analog input via RV1 or Rv2 potentiometers. Basically these potentiometers form a voltage divider that is feed by the 5V supply.
Disconnect the jumper2 SK2 and SK3 to remove the 5V supply. You can then input a voltage directly to the analog inputs and use the RV1 & RV2 pots to adjust the input voltage for a max readout at max input voltage (18V).
Problem here is that you will loose resolution if you just adjust RV1/2 as 18V would be dropped to 5V.
RV would form a voltage divider set to 27777 ohms & 72223 ohms. Applying 18V to the total 100K and extracting a scalled down voltage across 27777 ohms gives you 5 Volts (max input) to the op amp.
However drop that voltage to 12V with the same RV settings and you get 3.3V so your readings would go from a low of 168 @ 12V to 1 high of 255 @ 18V. Your 8bit ADC (analog to digital converter) effectively becomes a less than 7 bit ADC
What you really need to do to get the full scale of your ADC is add an offset voltage to counteract the voltage at the lowest input value (12V) and adjust the GAIN of the opamp to scale the 6V swing (18-12 = 6) so that the voltage swings from 0V to 5 V to give you a full 255 count from min to max inputs
The schematic shows that the gain of your op amps can be changed by the R8 & R9 values. See the instructions on Page 10
I would suggest that rather than messing to much with your board that you use an input conditiong circuit to elimeinat the DC voltage offset and hand the gain adjustment. This leave your USB board untouched at 0to5V inputs.
You can buy an instrument amp at digikey for less than 50 cents
http://search.digikey.com/scripts/DkSearch/dksus.dll?Detail&name=NJM4558D%23-ND
Wire it up as a differential amplifer where you input a 12V reference and your 12V to 18V input.
http://en.wikipedia.org/wiki/Differential_amplifier
Op Amp Data Sheet:
http://focus.ti.com/lit/ds/symlink/tlv272.pdf
part is available at www.digikey.com while supplies last.