Can someone tell me what I could be doing wrong?
Double-check all the wiring, the polarity of the electrolytic capacitors and whether the IC is properly placed (i.e. pin 1 is where you expect it to be)
Then, as KE7GKP
suggested, you can connect an alternative audio source at the input and / or use a small speaker at the output. Note: Do NOT connect a speaker or a headphone directly to the output (pin 5) - you need to add an output coupling capacitor there.
As extra information: I left out the capacitor on pin 7 of the IC that is shown in the schematic.
This is probably fine, but you can always try adding it back to see if that helps :-) The capacitor value does not have to match exactly the one in the schematic.
Also, how do you tell the anode and cathode on an electret microphone? (I tried both ways)
One of the leads of the microphone should be connected to the outer shell. This is the negative one (goes to ground).
I've had my share of troubles with a similar LM386 setup and have put my build-notes at http://lowvoltage.wordpress.com/lm386-mic-amp/