Only a few parts are required since the Feather has much of the functionality built-in.
There are three sections.
The entire circuit is powered through a 2.1mm DC barrel jack to which you connect the 12v power supply. As is best practice with a longer NeoPixel strip, there is a 1000 microFarad capacitor between 12v and ground. This reduces the initial sudden surge of voltage that can cause damage to the NeoPixels. Unlike most NeoPixel products, the strip used in this project is powered by 12v. The filtered 12v is attached to the strip. The Feather, however is powered by 5v. To accomplish this we need to use a 5v regulator as shown.
The power for the "neon" NeoPixel strip is, as mentioned, connected to the 12v. The data-in of the strip is connected to A0 on the Feather.
For flexibility and ease of mechanical design, the Feather's USB connection isn't directly exposed. Instead, an extension is made using a micro USB jack breakout, a DIY Micro USB plug, and a 10mm (4in) piece of 5-wire ribbon cable. This is cut from the 10-wire ribbon cable listed. The easiest way to get the connections right is to insert the plug into the socket and check the connectivity as you go.