How is this piezoelectric effect converted to voltage?
The typical way this is done is by measuring the flow of charge (current) from the device into an inverting amplifier circuit: -



Analog Devices app note CN0350 is where this circuit came from and here is a brief extract from that page: -


  Piezoelectric elements are commonly used for the measurement of
  acceleration and vibration. Here, the piezoelectric crystal is used in
  conjunction with a seismic mass m. If the mass is subjected to an
  acceleration a, then there is a resulting inertial force F = m × a
  acting on the seismic mass and the piezoelectric crystal. This results
  in the crystal acquiring a charge q = d × F, where d (measured in
  coulombs/newton, C/N) is the crystal charge sensitivity to force.
  
  The resulting steady-state charge sensitivity Sa of piezoelectric
  accelerometer is Sa = Δq/Δa (measured in C × s2/m).
  
  Note that acceleration can be converted to g using the relationship 1
  g = 9.81 m/s2.