Soldering

Below: Using a wire stripper set to 22 gauge, strip about 1/2" of plastic insulation:

Splicing two wires is made easier with masking tape to hold the wires in place while soldering:

Add heat shrink tubing over the splice to insulate:

Below: Blue masking tape holds everything in place when soldering wires onto a Neopixel strip.

After soldering, some hot glue can be added to add strain relief to the connection.