The voltages and wave forms applied to a LCD display can be quite complex - from 1 to 4 different wave forms/voltages to the 'rear' [for want of a better term] and ones opposite or the same to the segments on the 'front'.
To get a handle on how these work and how complex they can be, the best place to look may be a microprocessor that can run this type of display.
Since I'm a PIC person [no aspersions on other brands], I would suggest you download the PDF file of [as an example] the PIC16F1937 at:http://ww1.microchip.com/downloads/en/D ... 41364E.pdf
Section 27, specifically section 27.9 deals with the type of wave forms needed based on the type of LCD display.
Be warned, it is not something for the faint of heart.