By default, the amplifier breakout is in digital mode. To put it in analog mode we need to close the three solder jumpers labeled Analog, AD1 and AD2.
Now place the potentiometer that came with your kit into the three holes labeled Pot Vol - don't solder them in yet, try to just touch the pads to the pins so that you can adjust the volume. As you twist the pot, the volume will go up and down
Once you have that working, you can solder wires to the Pot Vol pads, so you can place the volume adjustment pot elsewhere (say mounted to the outside of a box)
If you want a potentiometer that will fit exactly in the slot, check out this side-adjustment pot http://www.digikey.com/product-detail/en/bourns-inc/3362M-1-103LF/3362M-103LF-ND/1088401
For mounting onto a box or panel check out https://www.adafruit.com/product/1789