How can I grow my own yeast (sourdough starter)?
Most bakers refer to this as a starter and it is extremely easy to keep up.  You will need a plastic bag or a jar to keep it in, a cup of warm water, and some flour.  You can either grow some wild yeast or add a particular strain to the growth solution depending what you are trying to do with the yeast.  Once you do that, just leave it someplace warm but not over 100 degree F. Then once a day, you feed the yeast by removing half and adding back a half cup of flour and a half cup of water.  Once it starts foaming remove to the fridge and remember to feed once a week.  It will be with you for the rest of the your time on earth.

Also, that half you take out when you feed it? Makes a great gift to other baking or cooking friends.  Also, if you devolop a dark smelly liquid, just stir it back in, it is normal and nothing to worry about.