Yale University
Yale University: Categorical Data Examples
Site provides some different examples of categorical data and discusses the use of two-way tables.
Texas Instruments
Texas Instruments: Testing Goodness of Fit and Two Way Table Chi Square
Students perform chi-square tests to see if data follows a hypothesized distribution. They also study the two-way table analysis.
Other
An Introduction to 2 Way Tables
Site has an example problem worked through showing how a two-way table is constructed, read, and used. Discussion then continues with a handful of learning exercises for the user to practice.