Amplifying Audio signal for use with TIP31 power transistor and LED array

I assumed that 0V means ground,

No.

First off what op amp is it?
What sort of microphone?
0V is the bias level, it is only ground if you are supplying the op amp with a negative supply as well as a positive one.
It is normal to create a 0V by having two 1K resistors between + and -, the junction creates a 0V.
There should be a resistor, say 10K from the +ve input to the 0V.
The pot should be connected to 0V not ground.
Depending on the type of microphone you might need a capacitor to couple it an and some DC bias fed into it. The other end of the microphone goes to 0V and not ground.