Most of the time when I make bread I use purchased yeast. But, because bread is an essential part of our diet, I wondered years ago what I would do if I couldn't buy yeast. (Yes, I was even thinking of things like that back then. :-}) A long time ago I was looking through someone's old German cookbook and came across a recipe for homemade yeast. I was very interested and copied the recipe down even though I was disappointed to find at the end you added the mixture to yeast you already had going. I wanted to know how to start from the beginning and felt it must be very difficult and mysterious. Several years later I read an article that mentioned capturing yeast from the air. Once again, I thought it must be very complicated but definitely wanted to learn more. After taking the time to learn more, I found that it wasn't difficult or mysterious at all! It can be as simple as putting equal parts of flour and water in a bowl, loosely covering it, and feeding it each day for a week.
If you already bake bread you will have plenty of wild yeast in your kitchen to capture. If not, you can crush unsprayed and unwashed grapes in cheesecloth and add that to your flour and water mixture. Grapes have a lot of yeast on them. Or, you can use whole rye flour for your mixture because it too has a lot of the naturally occuring yeast. (If you do one of those two things go ahead and cover your mixture well because you won't have to capture any from the air and won't have the skin form on top that you do when it is covered loosely.)
You will also have friendly bacteria called lactobaccili in your starter. They break down the simple sugars in the flour and that is what the yeast feed on. (That's why you have to feed your starter at least once a day, so there is new food for them. If there is little or no food it affects them just like it would us!) When the yeast feed on the sugar they produce carbon dioxide bubbles that stretch the gluten and that raises the dough. Pretty great, huh? The lactobaccili produce acids which give it flavor. There are many strains of wild yeast and bacteria that grow around the world so flavors vary. San Francisco is known for a very sour flavor. In other areas the taste is milder.
Some sourdough starter recipes call for adding a little commercial yeast. This isn't a good idea because the commercial yeast will compete with the wild. Another factor is that almost all of the lactic acid is gone in the commercial variety so you won't get the flavor. Some things just can't be rushed. Also, some say to add a little sweetener to the mix but this also isn't a good idea. You will have an imbalance of the yeast and bacteria and it isn't necessary.
(I read that goldminers used to sleep with their starters next to their bodies to keep the starter warm. Sounds like mighty important stuff!)
You can preserve the starter by pouring a thin layer out on parchment paper and letting it dry for a few days. Then peel it off and store it in a tightly sealed container. When you want to get it going again, dissolve the pieces in water and feed it for a week.
In case you're interested, here is the recipe that I copied so long ago for homemade yeast:
Add 4 potatoes to 2 quarts water in kettle. Add a handful of hops that have been tied up in a bag. Cook until potatoes are done. Remove bag, squeeze dry, and throw away what is left in bag. Put the squeezed juice in with the potatoes. Remove potatoes, mash, and return to kettle. Cool. Add 1 cup sugar, 1/4 cup salt, and 1 cup old yeast (leftover from previous time). Let stand several hours and use.