Sourdough starter is easy to take care of, especially when you use stone ground flour with plenty of bran and germ in it. Highly sifted flour, white flour, or nearly white flour, are more difficult to work with. Flour with the bran and germ removed do not support a healthy yeast colony as easily as whole flour does.
Feed your starter every week or two at the ratio of 2 parts flour to 1 part water, and keep it in a covered bowl or jar in the refrigerator. For most home bakers, a weekly feed of 1/4 water to 1/2 cup flour is perfect. Ideally, you'd like to feed the starter a day or two before using it in a recipe.
Excess starter can be used almost anywhere that you would use regular flour. Pancakes and cookies are two great places to put your extra starter in. There is no reason to every throw away your excess starter.
If your starter ever shows signs of mold, discard any trouble spots and feed normally. Similarly, if it ever dries out just dig some soft starter out of the middle and resume regular use. If you do ever completely lose your starter, just make a new one by mixing flour and water and feeding daily for a few days. It will reach full strength after a couple of weeks, but can be used in as little as two days.
An earthenware bowl with a loose-fitting cover is the best way to store your starter culture. Plastic, and especially plastic with a sealed lid, seem to invite unhealthy mold into your culture. I have experimented with different containers, but I've always gone back to an old ceramic bowl, loosely wrapped in a plastic bag.