The oft cited example of birefringence is rhombohedron calcite. Lab-grown sodium nitrate should exhibit this property as well, because it shares the same crystalline structure as calcite. However, sodium nitrate crystals grown in this lab were insufficiently clear and large to perform observations. Calcite shown below.
The actual shape of the calcite used in the observation above is this (rhombohedron).
The incoming ray of light is broken into two rays (whose polarization is at 90 degrees to each other and whose velocities through the material is different--hence birefringence) that travel through and exit the crystal.
As the crystal is rotated, one ray remains stationary (the ordinary ray), and one traces a circle about the other (the extraordinary ray).