Drill the holes for the bulb, the switch and the push button.
Stain or paint the box.
Then attach the PCB inside the box and cable everything together.
The driver circuit fits on the PCB if you remove three legs of it and connect the ground connector with a short wire.
See picture below.
Attach the batteries and switch the power on. Do not have the PICAXE chip in place yet!
Connect a wire to + connector of the batteries and tip to input pins of the driver circuit. The LEDs will lit.
If the driver circuit works fine, switch the power off, insert the chip and start programming.