How can I determine the frequency of an audio signal in a circuit?

What you need is a phase locked loop. This will give a square wave of the same frequency as the fundamental. Then feed this square wave to a port on the microprocessor, and use the on board TPU to measure the frequency. (The Atmega 128, among others, has a TPU). The LM565 is a good phase locked loop for the purpose (costs around $2 from Digi-Key).