Kombucha, like any other living thing, has a strong will to survive. If you start out with a bottle of store bought raw, unpasteurized Kombucha (you know the kind), you can get a fully functional mother culture within a week. It's cake. In fact, you would probably have to try pretty hard to NOT get a fully functional mother.
Also, if you are into things like taking down the man and Thoreau, this is a baby step to self reliance. Almost.
Step 1: Materials
1. A bottle of raw, unpasteurized Kombucha. I won't name names, I'll just say avoid the kind with juice added. I started mine with the ginger flavored one, but that wasn't my first choice.
2. A clean glass jar, preferably rinsed out with boiling water prior to use. Preferably a small one with a rather narrow throat.
3. Tea. Black or green, as long as it's got no additives. I used some kind of green tea in a tin with no English writing, and it worked just fine. My last culture I did with black tea, worked just fine.
5. Cheesecloth or similar cloth. I use sterile gauze I pilfered from a first aid kit and it works just fine.
Step 2: Step One: Make Sweet Tea
Make sweet tea. Brew some tea like you normally would for yourself. Teabags, loose-leaf...whatever.
In the jar you intend to start your culture in, pour in a few tablespoons of sugar
Step 3: Add your tea to your kombucha
Dump your entire bottle of store bought kombucha into the jar you plan to keep it in.
Then, fill up the jar with the sweet tea from the previous step. Add as much tea as you need to get the level of the liquid somewhere within a half- to quarter-inch of the top. As close to the narrowest part of the jar as possible.
Sample the concoction, make sure it tastes properly sweet.
Top with cheesecloth and put it in a warm or at least room-temperature place where it can sit undisturbed for a while.
Step 4: Wait wait wait
After a few hours, all of the gunk that you normally see at the bottom of your kombucha bottle will begin to organize into larger clumps and float to the top. Overnight this foamy thing will turn into something not unlike a man-o-war jellyfish. If you poke and prod your little jellyfish you'll notice that it's spread out across the entire surface of the tea with little a little invisible film. In the next couple of days this film will get thicker and thicker and take on the appearance of the familiar mother culture you've all seen pictures of on the internet.
Within the week you should have a small but thick and durable culture. In colder climates this may take longer, but that's remedied by just keeping it in a warm spot.
Step 5: A summary
Honestly, if you don't want to follow all those steps just open a bottle of kombucha you got from the store, secure a piece of cloth over the top with a rubber band, and let that sucker sit around for a week or two. That will do essentially the same thing, only I like to think the extra tea and sugar speed things up.
Step 6: Brewing future kombucha batches
Since I always just go with my gut instincts when mixing my tea and sugar, I get radically different results with each batch of kombucha I make. Before moving your tiny culture into a larger container(where it will get HUGE by the way) I recommend looking at other instructables for a good, consistent recipe.