If you need the static value, I would measure the capacity C of a condensor. You need 2 plates (electrodes) and a cuvette filled with the liquid. You measure the capacity with and without liquid. The ratio is epsilon. I would select a ac-method to determine C.
For high frequencies, the measurement of the velocity of light is a usual method. Here, the phase shift between 2 beams, one within vacuum (or air) and the other in liquid gives the result.