If you do some web searches on "kambucha", or "kombucha", you should find a lot of information about it, so I won't duplicate what you can already find. The wikipedia has a pretty good overview. I'll just list my recipe and state my two cents worth.
In a clean pot, I boil about 3.5 quarts of water. Then I turn off the heat and add 1 cup of sugar, about 3 tablespoons of green tea (usually gunpowder), and 3 tablespoons of black tea (often Lipton tea bags). I wait for this to cool until it is warm, but not hot to the touch.
Next, I strain this mixture into a very wide mouthed tinted jar that can hold at least a gallon. The main thing is just to have a large, wide mouthed jar. I add in about a cup of already made kombucha tea to increase the acidity. Finally, I add in the kambucha "mushroom" and cover with a cotton cloth.
How long you ferment the mixture depends on the temperature. For me, this means that the tea finishes faster in the summer. It will usually be ready in about 6-10 days, although I sometimes leave it longer for a sharper, vinegar-tasting batch.
I've tried making it with ginger tea. This works but I don't like it as much.
Is Kambucha a panacea? Does it live up to all of the hype you will find on the web about it? No, of course not. I think most of its benefits are similar to those of drinking a small amount of apple cider vinegar in the morning. So, I take a few ounces in the morning mixed with water and believe I derive mildly improved digestive benefits. I'm not ruling out additional benefits, but I haven't seen any convincing evidence of them. I like the taste a lot though and do think it is a generally healthy drink.
May as well add some more info here as I still get a lot of email questions. First you want a nearly constant temperature while fermenting, warm, but not hot. That's why on top of the fridge works well. Next, if you get any kind of mold in a batch then throw everything, including the liquid, away and start over with everything cleaned with a weak bleach solution. Finally, if you have problems with fruit flies, use sticky traps nearby to keep them down. They are attracted to the fermenting smell. Make sure your cover is snug so they can't get in. A yellow plastic cup with sticky goo on it works best, but regular fly paper should also do the trick.
UPDATE 2/07 -- Been quite awhile! I should have a new mushroom soon and will be making some new batches again. And I'll give away starters once I get going again. In the meantime, I've found a good commercial kombucha: "GT's Kombucha", which can be found at Whole Foods. I like this one even better than the popular brands available in Austria and Germany.
http://www.oocities.org/mdonath