After much frustration with the Perl implementation of neural nets, I went searching for other resources. Finally, I found the book AI Application Programming and started digging in. While there were a few things that I wish were clearer, I really can't complain too much. This is an excellent book! The chapter on neural networks covered a feed forward neural network with backpropagation learning. Essentially, you have a network of nodes (or neurons), give them some training data and run it through the network (feed forward). When you check your results, compute your error and walk back through the neurons while adjusting the weights of the connections (backpropagation). All in all, I found that it was a heck of a lot simpler than I thought.
The author gives a fairly clear example which I typed in by hand to ensure that I got it and, after a fixing a few typos, I had a simple neural network that determined what a game character would do depending on the characters health, weapon at hand and number of enemies. I also discovered that when I skipped the diagnostic output, the 20 second run time (which accounts for training the network) dropped to almost nothing. Whoo hoo!