There's a recipe on this page, geared towards someone without brewing experience, so it should be a breeze for a homebrewer. I haven't personally tried it though.
It is a shorter, simpler brewing process that that of beer. You could make it with a homebrew equipment kit.
For carbonation, if you follow their recipe, you run the risk of making bottle bombs. Most recipes I've seen recommend using plastic bottles, transferring to a fridge when the carbonation is right, and drinking the soda within a few weeks before it carbonates further.
A safer, quicker, and more reliable method would be force carbonation with a keg system, but that will obviously have a higher equipment cost.