Zeta potential can be measured by electrophoritic light scattering which uses laser Doppler measurements of light scattered from particles moving in response to an applied electric field.
In order to measure the zeta potential of your sample in dispersion, it may be required to dilute the sample, which should typically be done using the sample liquid as used to suspend the particles.
Zeta potential is a property of a particle within a dispersant system, so will vary with different ionic concentrations and pH.
The following link gives a good over view of what zeta potential means and how it is measured-