Sourdough starter is wild yeast, cultivated in a mix flour and water. If you've ever dissolved some bottled, store-bought yeast in water and watched it puff up, then you know roughly what sourdough starter is like. The difference here is that you're feeding the yeast every so often with more flour and water to keep it going.
So: how do you go about acquiring your own starter?
Of course, you could order some starter online, or get some from a friend. But why let someone else have all the fun? The basic idea is to mix together roughly equal parts water and flour and wait for the yeast to take up residence. In practice, of course, there are a couple more steps you can take to increase the likelihood of success. Each baker has a different idea of what works best for capturing wild yeast, but here's the strategy I've settled on, combining some King Arthur Flour tips and experimentation:
Start out with three or four ounces each of whole-wheat flour and lukewarm water (either bottled water or the filtered stuff—yeast is a living thing, and just as you don't use tap water with goldfish, try to avoid it with yeast). Use a very clean glass or ceramic container, preferably one just out of the dishwasher or scalded with boiling water. A pinch of sugar or a drop of molasses or honey stirred in to the slurry will give any yeast stumbling upon the slurry an extra jolt of energy. Cover your container loosely and set it in a warmish spot.