Sourdough is generally considered wild yeast, though it is actually a mixture of yeast and lacto-bacteria that together form the flavor of sourdough. The yeast however is the leavening, and thus more important for cooking.
The flavor and nature of a given sourdough depends strongly on the location. The famous San Francisco sourdough grows only in (and near) the city of San Francisco; if taken elsewhere the local yeasts and bacteria will soon grow, and in a few months it will no longer be San Francisco sourdough, but sourdough of the new location. For this reason, sourdough fans often trade batches with locals every few months, to get a flavor or yeast action that cannot be had locally.
Because each local variation is different, rising times and flavors are different. Thus some, though not all, batches can take up to a full day to rise. This will also affect the flavor.
Cooking with sourdough must be planned days or even weeks in advance to ensure sufficient starter is on hand. Bread can take 3 days between starting and baking, not counting time to prepare the starter.
Sourdough starter is alive. Thus the easiest way to get starter is find someone with it, and borrow a small amount and increase it. If you wish to have a starter other than whatever is local, this is the only way to get it. You can get a free sourdough starter that has been kept alive for 150 years from the Friends of Carl Griffith.
Making your own starter
If you cannot find a source of starter it is easy to make your own. Here is how it is done:
Bleached flour or tap water can be used, but these may give undesirable results. Chlorine in tap water can kill the wild yeast that you wish to grow. Bleached flour has most of the yeasts killed.
Combine 1/2 tablespoon of flour with 3 tablespoons of water and let sit overnight at room temperature. Each day add 1 tablespoon of water and one tablespoon flour and mix until the total volume is about 1 cup (240ml). The symbiotic combination of yeasts and lactobacilli can be encouraged to reproduce more easily by controlling the pH (acidity) of the mixture using pineapple juice instead of water for the first three days and maintaining a temperature of 75 °F (about 23 °C, roughly international room temperature). Make sure that you have a working starter by observing whether the dough bubbles and rises. If not, then leave exposed to the air and test again. Thereafter, dump out ½ cup (120ml), and mix in ½ cup (120ml) water and ½ cup (120ml) flour. Starter will be ready in 1 or 2 weeks, though the longer the better. There is a noticeable difference between a 1-week and a 1-month starter, and some can tell a difference between 1 month and 1 year. Some will claim it takes 40 years to get a good starter, though nobody waits that long to use it. The exact volumes used above are not critical. Use whatever measure you consider useful.
The above open-air method takes patience. You may have to repeat this procedure several times as there is no guarantee that you will pick up good yeasts floating in the air (there are many yeasts, but most will not make for good bread). The only way to tell is to wait until you get a critical mass of yeasts and see if it makes good bread. Generally, bad yeasts will smell strange. Your starter should always smell clean, perhaps with a sharp touch of alcohol/acid if it is getting old.
There is a second method that is more likely to succeed, but you lose the locality effect. Take some organic grapes. Wash them to knock off any dust or dirt, and immerse them in a bowl of clean water (as above) for 2 minutes. Remove the grapes from the water, which now contains the yeast that was growing on the outside of the grapes. If the grapes are local, then you have a local starter. Use ½ cup of the water and ½ cup flour to make a paste/dough, place in a small cup, cover and wait. If the dough rises, then you have a working starter. Build by doubling until you reach your desired volume.
A third method is to use a little kefir to initiate the sourdough starter. As with grapes, you will not get the effect of using a localised starter, but it is a reliable and effective method. Mix ½ cup of water and ½ cup of flour to make a paste/dough, add ½ teaspoon of kefir, mix well, and set aside to ferment. Give it a stir every eight hours or so. It should be very active within 3 hours, possibly as few as 2.
Mixing 100g flour with 100g buttermilk or natural yoghurt, plus 1 tbsp water is also very effective for beginning a sourdough starter. This usually takes about 72 hours at room temperature to get going.
Or if you really want to cheat, you can mix flour and water (half and half by weight) with a pinch of shop bought yeast. This should be left for 48 hrs at room temperature before using. You won't get the same natural taste initially, but the local yeasts in the air and in your flour will take over in time.
Pineapple juice mixed with flour and water is also claimed to be an effective way of beginning a new starter.
Sourdough starter is alive, and thus it must be fed regularly. When not using your starter, it is important to dump out half the batch from time to time, and mix in fresh flour and water to equal the lost volume. Exactly how often this should be done depends on storage temperatures and the local strain. An active starter should be fed daily (if not multiple times per day depending on temperature and other conditions). See the note below about dormant starters.
Sourdough is best stored at room temperature or slightly warmer. Anything outside of this range will change the proportions of the bacteria and yeast, which affects the flavor of the result. It can be safely stored in the fridge, but temperatures over 80F are too hot. If you store your starter in the fridge, then let it sit out several hours after feeding before returning it to the refrigerator. This allows the yeasts to get active and feed. The temperature in the fridge is enough to slow down the yeast, but not the lacto-bacteria. So after a while your starter will begin to smell boozy and have a sharper tang to it than you might want. To fix this, just dump out 90% and start the feeding cycle again.
Long-term storage can be done by drying some starter, causing the yeast to go dormant. Exactly how long yeast can be stored this way varies, but it is enough for trading starters. Freezing the dried-out starter allows it to be stored for over a year. Just dry the starter out, put it into a sealed jar and put it in the freezer. If you need it again, take one part of frozen starter, crush it, and mix it with one part of fresh flour. Add water and it should get active in a few hours.
If you do not bake daily, then your starter will go dormant as the yeasts shut down from hunger. You may see a separation occur in the starter vessel, where a yellowish clear liquid rises to the top and the white doughy starter falls to the bottom. The liquid is rich in yeast metabolic by-products. You can mix it back in when you feed, but it sharpens the finished bread flavor to a degree that you may find distasteful. Simply throw out the liquid before feeding. But you should note that once your starter has gone dormant, you must re-invigorate by multiple feedings to get it back to a healthful vigor (see below).
Using starter is easy, just take out the amount you need, and then mix equal parts flour and water to get back the original amount. Avoid using all the starter on hand, though if you must, enough will cling to the sides of the pot to get the starter going again.
If using starter often you should keep your batches large enough so that enough is on hand. If you rarely use your starter you should keep just a small amount on hand, and increase it before needed.
You need to make sure that your starter is full strength before committing it to a dough. That means that it should quadruple if fed and left for an hour. Feed starter and put ¼ cup in a measuring cup. If it hits the one cup marker in an hour or so then it is ready to go. If not, then it needs to be fed. Accelerate your feeding schedule until it passes the above test.
Many recipes call for more starter than is kept on hand. Starter is easily increased, just dump in more flour and water. It is generally best to do no more than double at a time. Depending on how vigorous your starter is it may take 2 days to get 4 cups from one cup (see above). (Remember to leave enough leftover for the next batch of starter though.)