There are stories of sourdough "Mothers" living for 150 years, being shared one cup at a time and keeping the family going, generation after generation. Fact or urban legend? Wagon trains crossing the country in search of gold and a better life, made sure they always had a sourdough "Mother" sponge aboard. San Francisco Sourdough Bread is probably one of the most famous breads made with sourdough. Friendship starter is another term used by friends as they shared a crock of the starter with a new bride or neighbor. A little card with recipes and wishes for a happy life is attached with a ribbon.
Sourdough (or natural leaven) has been around for a very long time. Before yeast was sold in little packets, it was made with leftover potato water and flour. Some bakers use scalded milk before mixing. Others use a variety of flours, such as whole wheat or rye. Wild yeast can also be used. Different ingredients will change the taste of the sourdough, in turn imparting unique flavors to your baked goods. You can also skip the entire conception part and buy Vermont's King Arthur's classic Sourdough Starter and then maintain it.
There are plenty of recipes out there, but this is one of the easiest to make and care for. Experiment!
Now that you've created a life, you need to feed and nurture it. Some bakers give their sourdough a name, although that's really not necessary. At this point it's still a baby and needs to be cared for. After a day or two when it smells sour and tangy, cover and put it in the refrigerator. As it gets older, it will soon be called "Mother" and has to be replenished each time you use "her". If you use 1 cup of starter, then you need to put 1 cup back. Replace with 1/2 cup of flour and 1/2 cup water, mix in well, let her sit out for a while, cover and put her back in the refrigerator. Every now and then, add some potato water to help her along. You must remember to feed her often or she will get moldy and die. :-(
So, what can you make with this messy, sour smelling slimy goop? Plenty! Some good suggestions are; sourdough bread, sourdough carrot cake, pancakes, bagels, coffeecake and muffins, quick breads, brownies, buttermilk biscuits, cinnamon rolls and, well, you get the picture. Just about anything that calls for leavening can be substituted with sourdough and with a little tweaking, turn out delicious baked goods.
Here's a good recipe to get started. Sourdough Carrot Cake with Cream Cheese Frosting