I will like to know how to measure displacement using a piezooectric transducer

Piezos detect force, not displacement, so an indirect approach is needed, as follows.

For an object that is set into motion, a piezo transducer attached to it will produce an output voltage proportional to the acceleration of that object. This is because the transducer has mass, and F = mA. The time integral of the acceleration will then yield the velocity of that object.

This technique of deducing velocities from forces using piezos with calibrated test masses attached to them is very common and furnishes the basis for the design of modern solid-state accelerometers.

Integrating velocity over time will yield displacement too, but for best accuracy, extremely precise time measurements and force measurements are needed to feed the integration engine.

Stable, precision accelerometers combined with high-precision clocks form the basis in turn of inertial navigation systems as used in aircraft and ballistic missiles.