Remove the silicone sheathing from your NeoPixel strip. It's easiest to cut into it with scissors or diagonal cutters and then slide small sections off at a time.

Hold the strip up to your hat's brim to measure the length for the first piece. The design is up to you!

When cutting segments of strip to compose your design, you'll always have a "sacrificed" pixel. Cut close to the waste pixel to preserve the size of the solder pads on the neighboring pixels.

Cut three pieces to the desired length, using pins or masking tape to mock up your design on the hat.

Next prep three pieces of stranded wire (or one piece of three-channel ribbon wire) by stripping and tinning the ends.

To solder wires to NeoPixel strip, identify the input end (arrows facing away). First solder wires to + and -, then solder the signal wire on the opposite side of the flex PCB. This way your solder joints will be less likely to crowd each other.

Repeat for the remaining pieces of NeoPixel strip in your design, soldering three wires to each input side.

For places where the two pieces of NeoPixel strip will come into close contact with one another, wrap the soldered end in tape so the contacts don't short to the other segment. Tape/pin in place and carefully solder to the output end of the previous strip.

This is a tricky technique that can take practice to achieve a tidy result. You may want to test it out on scrap pieces of strip before soldering the pieces meant for your hat!

Likewise make the connection at the top of the cap, and stitch down any loose wires with a bit of plain thread.

Stitch your NeoPixel strip to your hat. You can use the holes provided or just stitch around the whole flex PCB. Near the brim of the hat, be sure to sew underneath the hem band. You only need to make a stitch every few pixels or so to keep the strip firmly following the contour of the hat.