We'll need three wires to connect the NeoPixel stick to the Adafruit Feather. I suggest using three different colored wires to help tell the connections apart. The wires will need to be 13cm in length. Use wire cutters to cut three pieces of wire down to size.
Tin NeoPixel Wires
Use wire strippers to remove a small amount of insulation for each of the three wires. Secure the wire to helping third hands. Tin the exposed tips of each wire by applying a small amount of solder. Use the tip of the soldering iron to heat up the exposed tip, then bring the solder wire close until it melts on the strands of wire. This will help prevent the strands of wire from fraying and makes it easier to attach them to the NeoPixels.
Next, we'll work on attaching the wires to the pads on the NeoPixel stick PCB. On the back, are two sets of 4 pads. Look for the pad with the label "DIN" (That stands for "Data-Input"). We'll need to tin three pads with a bit of solder. Apply a small amount of solder up to the 5VDC, GND and DIN pads.
Solder Wires to NeoPixel
Secure the NeoPixel PCB to third helping hands. Orient the PCB so that the wires can be soldered in-line with the NeoPixels. Heat one of the tinned pads with soldering iron tip and lay a corresponding wire onto the pad while the solder is molten. Lift tip and let dry. Repeat for the DIN, 5VDC and GND pads.
Feather to NeoPixel
Now we can connect the NeoPixel stick to the Adafruit Feather. We'll need to start by securing the Adafruit Feather PCB to the Panavise. To keep the three wires grouped together, you can use a piece of heat shrink tubing. Cut a small piece from the tube and slide the wires through. Using a lighter or heating element (not the tip!) of the soldering iron, apply heat to the tube and watch it shrink like magic.
Connect NeoPixel Wires to Feather
Apply a bit of soldering to pin #30, G, and 3V on the Adafruit Feather. Then, connect the DIN wire from the NeoPixel to pin #30 on Adafruit Feather. Connect GND from NeoPixel to G on Adafruit Feather. Then, 5VDC from NeoPixel to 3V on Adafruit Feather.
You will need to share the G (ground) pin on the Adafruit Feather with the ground wire from NeoPixel and the switch.
And now we have our final circuit! We're done with all the wiring, we can now work on mounting the components to the 3D print. Double check your work and ensure all of the connections look solid.
Now is a good time to test the circuit! If you've uploaded any code to the Adafruit Feather, you can connect the battery and engage the switch to power it on. You'll need to conduct your own testing, depending on the sketch your running. In this example, I'm testing out the bluefruit control using the Adafruit Bluefruit Connect iOS app for iPhone and the NeoPixel Picker arduino sketch (the one included with the bluefruit nRF52 library).