The Wikipedia article on DSP has some good links to textbooks in its Further Reading section. Some Universities also make their course notes available online, which you should be able to find by Googling. Most CS DSP modules should give you a good grounding in signal processing.
You want it to detect the sound of a dog barking. What kind of sounds do you not want it to detect? Once you decide what you want and what you don't want, then you need a way to describe the differences between these two types of audio signals in mathematical terms.
you would probably have to learn about dog barks a little first then, you will have to identify the bark frequency for the ipod to recognize, this will probably be pretty tough too just letting you know
It's actually a pretty hard problem... I'd approach it using a hidden markov model to do the actual detection. To get sound in from the mic I'd go with AudioQueueServices.