The gemma has a tiny on/off switch onboard. You can skip this step and just use that switch, but adding a clicky switch you can feel without opening up the scarf and looking inside can be really helpful.
Lithium Polymer batteries are wonderful things. They are small, compact and light and carry a lot of power, and will keep your LEDs running for a nice long time.
However, they do have their drawbacks -- it's good to know what the dangers are before you commit.
LiPo batteries are pretty volatile. If they get wet or get punctured, they can catch fire.. not a good thing when you've got them involved with your clothing.
They are also rather delicate. The batteries come with a handy JST connector, but the solder points going into the battery terminal are small and brittle. To keep them from breaking or doing anything dangerous, we need to add some strain relief.
I also like to add a switch to these batteries, as pulling the connector in and out of your microcontroller places wear and tear on the wires. Having a switch is easier and safer all around.
If you’re particularly safety-minded (e.g. if the scarf will be worn by a child), the LiPo cell can be replaced by a 3xAA battery holder, with single-use alkaline cells. The battery holder already has a switch built in. Add a JST connector by cutting and splicing one end of a JST battery extension cable. You'll need to edit the code to limit the brightness to a level the alkaline cells can sustain. Try a brightness value of 50 to start and work up or down from there.
Cut the red power wire in the middle and strip about 1/2" of insulation from each side. Strip the same amount from both leads of your switch, and slide some heat shrink on to each one.
Connect one lead to each power wire. Wind the wires around a whole bunch of times before your solder -- you want these connections really solid. Once the connections are good, slide the heat shrink down and shrink it in place.
Using a rubber band, secure the wires to the battery in such a way that tugging on the JST connector or on the switch doesn't pull on the wires where they connect into the battery. Don't use cable ties around the battery itself, or pull it too tight! You do NOT want to puncture this battery! We're trying to make it safer, not make it explode.
For good measure, add a blob of hot glue to the point where the wires connect to the battery to discourage them even more from disconnecting.