To try out the shortest path algorithm, you want four things:

• A data set: sample data files, 110 cities and 181 roads, available here.
• Knowledge of a good shortest-path-finding algorithm. Here's one, based on a Min-Heap.
• Knowledge of how to make that algorithm go: in this case How to use a heap.
  The detailed mechanics of heap operations are shown here.
• Some way of displaying the results nicely: dynamic creation of graphics files in CGI is shown here.

So there you are.