For instructions on how to make your own kombucha go here: Making Kombucha Tea!
After you make the tea just put it in a bottle or glass jar with a little fruit or juice and let it sit at room temperature for a few days to three weeks (the longer the more fizzy it will be). Leave a little room at the top so the bottle doesn't explode! And be careful when you open it.
Wash your kumquats, slice them in half, and take the seeds out. Add a few kumquat halves to a clean glass jar or bottle and fill the rest with kombucha leaving a little room at the top.