Follow the illustration above and to reference how all the components are connected. The diagram isn't to scale and doesn't display how the circuit show actually look like. The actually circuit is much more condensed and has rather lengthy wiring!

Below is a list of the components pin outs.

Powerboost 500C to Trinket
Male JST to Female JST

Powerboost 500C to Switch
EN, GND 

Trinket 5V to NeoPixel Strip
GND to GND, BAT to 5V, #0 to DIN

NeoPixel Strip to NeoPixel Ring
GND to GND, 5V to 5V, DO to IN

Battery to Powerboost 500C
Male JST to Female JST