This is a popular inductor and capacitor measuring circuit. It is based on measuring the frequency change that occurs in an LC oscillator when the unknown inductor or the unknown capacitor is placed in parallel (capacitor) or in series (inductor) with the built-in L and C oscillator components. There are many variations on the microprocessor used to measure frequency, but the oscillator circuit stays pretty much the same. Look at the schematic images
here for some idea of the variations. Compare with the PIC implementation in the image below:
Or this one, based on the popular ATMega:
The problem with the novice trying to duplicate any of these is usually the microprocessor code. The easiest solution is probably to measure the period of the LM311 oscillator output and use floating-point math functions to calculate the inductance or capacitance that caused the change in frequency. Or you could just
buy one that works without any additional coding required, but where is the fun in that?.