Awhile ago, my Food & Fitness instructor brought her kombucha culture to class. It was massive. She divided the scoby (symbiotic culture of bacteria & yeast) into pieces so anyone who wanted to make their own kombucha could have a piece.
I took a scoby piece home for kicks. The scoby needed something to feed on, so I brewed black tea (roughly 8 cups water, 4-5 tea bags) and sweetened it with sugar (3/4 cup).
After brewing, I waited till the tea cooled down to room temperature, then poured it into a clean jar (formerly of pickles) with the scoby and about a cup of its original liquid.
The jar was covered with a clean towel and left to undergo the aerobic (oxygen included) first fermentation. During that time the scoby grows thicker, the tea turns slightly sour and the whole thing starts to smell like apple cider vinegar.
10 days later I pour most of the liquid into a second jar, this time with a tight-fitting lid for the anaerobic (no oxygen) second fermentation. You can flavor your kombucha at this point - so far I have tried a capful of elderberry syrup (floral/fragrant and very pleasant), agave nectar (slightly spicy/smoky sweet) and honey lemon (still fermenting). You can use a variety of fruit purees or nectars to flavor.
Meanwhile I brew a new batch of tea to accompany the leftover scoby/liquid for another first fermentation.
5 days later I move the second fermentation to the refrigerator, to slow it down so it doesn't get too sour and fizzy on me. The fermentation lengths are something you can play with, both for the first and second fermentation. It's recommended to taste the liquid every day so you can see how you like it - the longer it goes the less sweet and more sour it gets.
If you're here in San Francisco, I'd be happy to give you a piece of my scoby. If you're not though, here's a good article to get you started with your own. Happy fermenting!