This illustrates a step-by-step easy method for brewing Kombucha tea. This is what I do. It is a lot easier than I thought it was going to be.
1.  I use a glass sun tea jar for brewing. This one contains a SCOBY (symbiotic culture of bacteria and yeast) and an inch or two of Kombucha from the previous batch. Your starter should include at least one SCOBY and vinegary Kombucha.
2. Bring to a boil, just enough water to brew about 6 packets of tea. Turn off heat, steep for 20 minutes. I use black, green or white tea. Feel free to experiment, but herbal teas have not been too successful. 
3. Remove the tea bags. Add about one cup of sugar, honey, or get creative. I've also used brown, raw, and molasses. This is what nourishes the culture. 
4.  Add cold water to the tea to cool it before adding it to the live culture. Too much heat can kill it. Chorinated water can harm the bacteria and yeast also. Bottled water or well water have both worked well for me.
5.  Add the cooled tea to the culture waiting in the jar. Warm is OK, hot is not. You can cool it overnight, but putting it immediately in the Kombucha culture will prevent the sugary tea from going "bad" or growing mold.
6.  Fill the jar leaving several inches before the top. If it is too full it will come out the top. Brown strings of yeast floating around are normal. Many drink the yeast strings with the tea, but I usually filter it out.
7. I cover the brew with a paper coffee filter to keep out dirt and insects. I have also used a clean cloth. I screw the plastic lid on. A rubber band also works. This is a good time to write the date on the edge of the paper filter. 
8.  Let it sit at room temperature for 9 to 14 days. You can draw some out through the spigot at any time to taste it. I often brew it for a month or more before bottling. It's quite vinegary, but I like it. I put it into plastic bottles and store it in the refrigerator. It can be stored at room temperature also, but it will continue to brew.


Lots more information on Kombucha (and kefir)>