This Sewable CR2032 battery holder is by far the easiest way to add a battery to a small wearable project.
There are two small 1mm diameter holes in the metal connection tabs, just large enough for a #5 or smaller needle to pass through. One tab connects to common ground (negative) and the other tab is +3 Volts.
This holder is meant to be used with Lithium CR2032 (20mm diameter, 3.2mm thick) sized coin batteries. These are almost always 3V at about 200+ mAh capacity. Lithium coin cells are not rechargeable but they are very easy to find, available at any grocery store.
Inserting the coin is easy, the holder is very sturdy, and it snaps out with a push. Its got a nice flat plastic back that you can easily glue in place for extra mechanical stability.