As far as I know ZnO film is a conducting material. So, we can presume that standard measurement techniques may be applied. The book recommended above is awesome and comprehensive, no doubt, but I'd like to advise look over a couple of Keithley's free classical and more simple handbooks:
By simply method ,you can deposit two electrodes (aluminium or gold film) on ZnO film directly and connect DC power with digital ammeter and voltmeter measurements by taking many of values.
You can deposit aluminium electrodes firstly on substrate by thermal evaporation, and after that you can deposit your material by using the same method with the mask. The region to measure the I-V characteristics must be small (some millimeter lengths)
ZnO has that time constant to light is very long time. So I think that, Firstly that device exposure to light or dark for long time. Next we need to investigate the time to ignore these effects.