Unwind the wires from the circuit playground and feed them through the hole on the lower right side of the 3d printed case back.  Solder them in place.

Feed the female end of your battery extension cable switch into the hole on the lower left.  Plug this cable into the JST connector on the Circuit Playground.

Nestle the circuit playground inside the case, with all wires feeding neatly underneath, and press down so the USB port lines up with its hole and the posts slot neatly into the Circuit Playground's holes.  Be sure the wires are feeding neatly and then secure the Circuit Playground to the posts with a dab of hot glue.

Place the lid inside the top and tape it in place.  Screw the top onto the base and then adjust the lid until the holes line up perfectly with the buttons.  Carefully remove the lid and top, and glue them together.

Turn the whole assembly upside down and place the buttons into the holes in the lid, face-down.  Screw or press the base into place.  Make sure the buttons work, then glue the lid down.

Using a strong acrylic glue, affix the belt clip to the back of the base with the usb port facing down.

Finishing

Find a convenient yet out-of-the-way spot for the switch and secure it to the skirt with glue and thread tacks.

Use some scrap fabric to machine or hand stitch a pocket for your battery.

Try it on under various skirts!  I like to wear it with the Circuit Playground clipped onto the outer skirt like a belt buckle, with the lights and wires twinkling beneath.

Another idea:  If you plan to wear this with full dresses in addition to skirts, you could add an extra 12-18 inches of wire between the circuit playground case and the top of the skirt.  Then you could wear the Circuit Playground as a brooch along your neckline instead of a weirdly glowing circle under the dress at your waist.  It's also possible to control the brightness of the Circuit Playground independently of the LED strands in the code, so play with brightness levels until you find a good balance.