Sourdough starters are essentially sources of live yeast, used to leaven (and flavor) various bread products. Sourdough starters have likely been used in this fashion for thousands of years; it is only relatively recently that commercial, isolated yeasts have become available. Because local wild yeasts tend ultimately to "take over" a starter, starters tend to vary in flavor and strength from region to region.
Some recipes I've read claim that people who live in the San Francisco area needn't add yeast to make a starter. I've never seen any proof that this is true... I do think that the admonition to never use any metal when mixing or storing the starter is a good idea, particularly when it comes to storing, as the sourness comes from various organic acids the yeast generates as it grows.
To make your own starter, dissolve a package of commercial yeast (either dry or refrigerated) in 1 cup of warm (not hot, but noticeably warmer than room temperature) water in a non-metallic container (it should be able to hold at least 3 cups). Add about 2 teaspoons of sugar. When the dissolved yeast "sponges" (that is, when you see a foamy mass on the surface), stir in 1/2 cup of flour. (Note: whole grain flours, with their higher fat content that can become rancid, tend not to do so well here.) The resulting starter should be rather thin, thinner than a pancake batter.
Leave the starter in a warm place, covered with a damp cloth. Stir it down from time to time, as needed. Keep an eye on it, particularly in the early stages, as it may tend to try to raise out of the container.
After one day, the starter should have slowed somewhat; the yeast has consumed the sugar, and should now be working on the starches in the flour. Most likely, you'll find that the starter has separated, with a top layer of clear liquid. Stir this back in, add another 1/2 cup of flour, mix thoroughly, and leave in a warm place as before.
After one day more, the starter is ready to use. To use, stir the separated starter to make it smooth, remove the amount of starter you need, then replenish it by adding more water and flour (in a 1:1 ratio). If you know you'll need more starter than usual the next day, simply add even more water and flour. Don't worry about small lumps in the starter, by the way; these tend to work themselve out upon standing. From this point onwards, store in a cool location.
Well-established starters have been known to remain active for many years. To keep yours going, be sure to replenish the flour (the source of food for the yeast) regularly. If you don't use the starter over a period of a 2 days, discard about 1/2 the starter and replenish as before.
If you know you won't use the starter for a week or so, you can try the trick we use. My wife and I have found that we can store our starter in the refrigerator for up to two or three weeks without replenishing. To use a refrigerated starter, bring the starter to room temperature before using.