Jack - Dumb question. I purchased it and it came in. Do I need a charger to charge the battery? Do I need to connect the battery when using? :) don't judge.
If you bought the particular one I linked, it should have come with a charger. (Mine came with the light, the battery, a charger, a pouch/strap to mount the battery to the bike frame, two rubber rings to mount the light to the handlebars, and a headband to mount the light on your head.) It's not a standard voltage, so yes, you'd either need that particular charger or some universal one with the voltage set correctly.
(Some other lights based on similar designs might have been designed for 5 volts and just come with a USB plug instead of a charger. Either way, every light should come with one or the other. If yours has neither, complain.)
Yes, you'll have to connect the battery to the light to use it.