The first step is to trim your NeoPixel strip into small segments. Measure out and cut seven sections with 8 LEDs per segment. You can use scissors to cut at the line running through a three copper pad section.
You should end up with four extra pixels per meter strip -- save those, you'll end up using three of them as the dots for the colon and decimal point.
In order to prevent mis-wiring, use a black marker on the back of each strip to indicate the ground line and direction from DIN to DOUT of the NeoPixels. Then, you'll make a jig to arrange them into the segmented digits.
Click the button to download the drawings needed to cut the acrylic panels on a laser cutter.
To keep the semgents aligned during connection and soldering, as well as to support the flexible digits in the final panel, you'll cut out a jig panel from 3mm acrylic.
Flip the panel over and arrange the strips with LEDs facing down in the jig.
You can now solder small strips of wire to make the connections from ground to ground, 5V to 5V, and DOUT to DIN between each strip.
Use the above photo as a guide -- the F segment will be the one connected via wire to the Arduino and power supply and you'll connect them in the order F-A-B-C-D-E-G. (Note: if you play this sequence on a pan flute you may summon a colored LED fairie.)
Soldering short wires works just fine, but to step things up a notch, I decided to mill small PCBs called NeoJoints that were designed just for this purpose by Tod Kurt. I used 82 degree and 98 degree joints to achieve the properly slanted segments. There is also one straight section where B and C join.
It's helpful to tin all of the pads with solder, then tape down all of the parts, and then heat up the solder with the tip of your iron to join them.
To get data from the Arduio and level shifter to the NeoPixels, you'll solder on a 3-conductor JST SM connector to the open end of segment F. You'll connect the center wire will to the DIN pin, with one outside wire going to GND and the other to 5V.
Choose one cable gender and one conductor to be GND consistently for all digits and cables -- I decided to place the female connectors on the circuitboard and the male connectors on the NeoPixels.
Use your soldering iron to tin each pad and wire, then solder the connections.
Slide the silicone insulator into place.
To keep things running smoothly and to avoid noise, solder a 1000uF capacitor to the strip. The first NeoJoint is an ideal location -- solder the capacitor negative to GND and positive to 5V line.
This digit is ready for a circuit that can control it!
For the three panels that have a dot for the colon or decimal point, cut a single NeoPixel from a strip and wire it from the end of the G segment over the 5V, DOUT, and GND pads to the 5V, DIN, and GND pads.