In order to measure a capacitance of a capacitor, there is many measuring method but perhaps the mot suitable one using a differential amplifier is to derive the capacitor by a voltage ramp dv/dt and sensing the current passing through the capacitor by inserting a current sensing small resistance Rm in series with the capacitor. Assuming that the current is ic, then the voltage drop across Rm ic Rm= Vm. This voltage can be acquired by the differential amplifier.
On the other side, by definition ic= c dv/dt. This result finally in
c= Vm/ (Rm. dv/dt). Then one calculates c by measuring Vm at the output of the differential amplifier. Both Rm and the voltage ramp dv/dt can be chosen to measure c with good resolution.
You need an oscilloscope. Configure the capacitor in an RC series circuit and charge the capacitor with a battery. Measure the time constant of the resulting charge curve. That will allow you to calculate the capacitance.