I concur with Corion that you need low-level tests to make sure each routine does what it should as well as end-to-end tests to make sure the pieces come together as you expect. For the latter, you might want to look into Apache::Test for which there is a tutorial here.

When I've been using Apache::Test recently for end-to-end testing, I've found it useful at times to override the final presentation phase of my web application. Instead of returning a text/html page with nicely formatted results, I return a text/plain response containing a YAML dump of the application's internal state. Obviously you also need to test that the formatted results work too, but a state dump makes it very easy to test actual vs expected results for a wide range of input values.