A huge body of literature has been devoted to the analysis of the one-dimensional CGLE (See Aranson and Kramer, 2002 and references therein). Hence, this tutorial is confined to reviewing the most elementary behaviours. We begin with an analysis of plane wave solutions to the CGLE, where long-wave stability results are derived. These results are subsequently complemented by the graphical results of numerical simulations, illustrating the instability behaviour. Finally, a range of other behaviours observed in the one-dimensional CGLE are elucidated.