How does 13 connections control a simple LCD with 34 segments?
It takes the right signals on both the top and bottom glass to "light" a segment (actually turns it dark, tranparent is the not-see case).  This allows LCDs to be arranged somewhat in a matrix.  A segment only lights when both leads are driven a particular way.  The other leads are driven in a way so that no other segment is lit.

These kinds of 7-segment LCDs are usually broken into a small number of "commons", and a larger number of segments.  Each individual segment is connected to one common and one segment line that have to have a AC signal between them for the segment to light.  For example, your 36 pixels may be driven by 4 common and 9 segment lines.

The LCD driver in the microcontroller automatically sequences thru producing the right signals on each common, then driving the selected segments for that common, on to the next common, etc.  LCDs respond relatively slowly, and this scanning is done fast enough so that a segment won't "unlight" (actually turn transparent again) in the short time between being activated each scan.

Look up a LCD datasheet, and you will see a map of the commons and segments, and which combination is required to activate each pixel.  Be sure to look at a "bare glass" LCD datasheet.  Unfortunately, complete LCD assemblies with driver chip are also called "LCDs".  Those you control by sending commands to the driver chip, which then does the multiplexing.

More commons forces more complicated waveforms, so the number of commons is usually limited to around 4 or 5.  Again, take a look at a LCD bare glass datasheet.  It may also be instructive to look at the datasheet chapter for the LCD driver built into a microcontroller.  Microchip PICs, for example, tend to have a "9" near the end of their part number if they contain a LCD driver, but you can also just look for one with a LCD driver in the selector guide.