A circuit's Power Factor is the ratio of the "Real Power" to the "Apparent Power", Pr/Pa. It is also equal to the cos(Voltage Phase Angle - Current Phase Angle).
It can be measured in an AC circuit by comparing the Voltage wave form to the Current wave form. If the voltage and current wave forms are not exactly in phase then there is a power factor < 1. So if you were to measure the zero crossing points of each wave form (voltage & current), you could then calculate the phase angle difference and the power factor.
For example, with a 50 Hz sine wave there is about 55.6uS per degree, (1/50/360). So if the measured wave forms had a difference of 1000uS this would calculate to a phase difference of 18 degrees, and the power factor would be cos(18), or 0.95