The recipe I used for my starter came from this website, and included a nice, encouraging video. Far more authoritative advice can be found here. What follows is my own personal experience with sourdough-from-scratch. Your results may vary.
Leavening bread without commercial yeast is surprisingly easy. The yeast is already in the flour naturally. I use a quality, organic stone-ground whole wheat flour from Outpost. Just to be on the safe side, I keep on hand a pitcher of city water that was allowed to sit for a day to let the chlorine dissipate (though some authorities say this isn't necessary).
Stir together in a plastic or glass box (never metal), cover loosely and let sit 48 hours at room temperature, stirring vigorously 2-3 times per day.
Cover loosely and let sit 24-48 hours at room temperature, stirring vigorously 2-3 times per day. If it is not bubbly after 48 hours have passed you may have to start over from scratch (maybe with a better flour).
Cover loosely and let sit 24 hours at room temperature
Starter mixture should have the consistency of a thick batter from here on out and is ready to bake with. The first batch of bread may not be very sour, the second batch may be more sour, but once it has matured the starter doesn't seem to produce progressively sourer bread. Hereafter you have to feed it once or twice a day or else put it in the fridge and remember to feed it once a week.
Feeding flour to the starter keeps the yeast alive and multiplying. The amount you feed depends on the volume of the mixture at any given time, and it doesn't seem to be an exact science. If I have a small container I feed it only 1/4 cup of flour at a time, but a larger batch I'll feed 1/3 or 1/2 cup of flour, and always add just enough water to maintain that thick batter consistency. If the starter has been in the fridge, allow it to come up to room temperature before feeding it. Then leave it at room temperature for 6 hours or so before returning it to the fridge. If you really aren't planning on baking for awhile you should decrease the volume of the starter before feeding it: throw half of it away or share it with a friend. If you don't reduce the volume you will have to feed it more flour, and you will quickly end up with more starter than you can handle.
I always feed my starter and let it sit for a few hours to get nice and bubbly before either starting a batch of bread or putting it in the fridge to suspend its animation.
One loaf of bread takes 3/4 cup of starter. I wait until I have built up the volume of starter over a cup so that I always have some left to build up for the next baking. I also like to bake two loaves at the same time, so I take the starter out of the fridge a few days early and build up a nice big batch.
I always use whole wheat flour to feed my starter, even if I will end up baking with mostly white flour. Whole wheat adds so much flavor, and all-white sourdough bread is too boring to bake at home--if you want it you can always find it in a bakery.