How do I change the output volume of this audio amplifier circuit?
Since this circuit requires both positive and negative power, you can place a pot either before of after capacitor. If you had a virtual ground (for example made using two resistors),  you would want to place the pot before the capacitor.
Reduced power will reduce output, but halving the supply voltage will decrease the output power by more than 50%. Both devices are may operate from +5/-5V power supplies; however Figure 6 in TPA6120 datasheet shows that distortion-free power is 0.5W for +-15V, and 0.05W for +-5V (into 32ohm speaker).