  The combination of the group ring setting with the methods of character
theory allows an elegant and powerful analysis of various combinatorial
structures, via their character sums. These combinatorial structures include
difference sets, relative difference sets, partial difference sets, bent
functions, hyperplanes, spreads, and LP-packings. However, the literature on
these techniques often relies on peculiar conventions and implicit
understandings that are not always readily accessible to those new to the
subject. While there are many excellent advanced sources describing these
techniques, we are not aware of an expository paper at the introductory level
that articulates the commonly used ``tricks of the trade''. We attempt to
remedy this situation by means of illustrative examples, explicit discussion of
conventions, and instructive proofs of fundamental results.
