Back in 1849, people from all over the globe flooded into Northern California, looking for gold. (That was the Gold Rush.) Not everyone got rich.
Damned few got really rich, and most got hungry.
Hungry miners bought simple food they could fix themselves, including flour for bread. (And that is the way to make money off of a gold rush: sell stuff (picks & shovels, flour & bacon, booze & pussy) to miners.)
Yeast to make the bread rise turned out not to be a problem; there are wild yeasts in the San Francisco Bay Area (that most miners traveled through, to get to the gold fields) to this day that make the classic sourdough bread it is famous for.
You can keep a pot of live yeast culture alive in a flour & water medium (some folks add sugar or honey, or potato slices to feed it, but it's not necessary).
You'll need a pottery crock (the kind you'd marinate Sauerbraten in), or a large glass jar. (You can use a plastic container but dear GODS, why. You are using an ancient foodmaking technique; show some class.) You can cover your crock with a cloth and a rubber band if you're nervous about it escaping.
You should use a wooden spoon. Not metal.
Mix one measure of flour with one measure of water-- in crazy, ill-conceived American moon units, two "cups" of each. The proportions matter more than the absolute amount.
Put the cloth over the top and leave it on the kitchen counter. Out of thin air, it will have been contaminated, I mean, graciously inoculated with yeast that floats in your house, and which will now grow and divide in the privacy of your crock.
Within a few days, the brew will become frothy as the yeast population increases. The froth is caused by carbon dioxide that the yeast is generating as it digests the flour; the starter will also have lactobacilli, a harmless bacteria, in it. This gives the bread that slightly acidic flavor by creating lactic acid. Alcohol is also involved <.< >.>
The flour soup doesn't get infested with mold & bad bacteria, becoming a disgusting health hazard, because the starch in bread flour is something that not a lot of bacteria can easily handle. Yeast, though, is pro at this: it creates special enzymes to deal with starch. The yeast & lactobacilli also "poison" the culture with the alcohol and lactic acid they produce, and that keeps other bacteria out. You will smell this happening; do not panic.
Leave the starter on the kitchen counter for five days. Feed it after 24 hours and every one or two days thereafter by dividing it in half and adding "a cup" of flour and "a cup" of water to one half of it (you can throw the other half away, or put it into your soda bread). When you see a watery substance-- the "hooch"-- floating to the top; stir it back in. Over the week the starter will get like pancake batter. It will be slightly yellowish. It is ready TO TAKE OVER THE WORLD.
At this point you can do one of two things:
You can store it in the refrigerator to slow down the yeast. Then you will only have to feed it every 5 or 6 days.
Or, keep it on the counter and feed it every day. Flour might be in short supply, so I recommend the first.
To use it in baking, add "a cup" of this culture to your dough instead of the packaged yeast your recipe calls for. Replenish the pot by adding back an equal amount of flour and water, and it can stay alive long enough for you to hand it down to your grandchildren. (The Boudin bakery here in San Francisco is still using the original dough that's been used in every single loaf of their bread in the last 160 years. During the earthquake and fire of 1906 the culture was saved, carried out in a bucket. Yours, too, can be immortal.)