There are plenty and myths and misconceptions about creating sourdough cultures. Here's what you need to know to start.
What you're doing is creating an environment where microorganisms, already present in nearly all grain, are encouraged to grow. To do this, we encourage the beneficial microorganisms we want while discouraging ones that are less satisfactory. Nothing more or less.
Yeast lives to digest the starches in grains, producing Ethanol and Carbon dioxide as byproducts. Consequently they are nearly always present on grain crops unless pains are taken to sterilize the grain. I've produced nearly identical starters working in Chinese kitchens that have never seen yeast, home baking not being a common hobby in China, as well as kitchens where baking has been going on for years. The yeast on your flour is highly evolved to eat the flour it's on, and wakes up hungry as soon as it meets moisture.
Fundamentally, sourdough starter is nothing more or less than a fairly runny version of yeast dough. Like all yeast doughs, it's fairly forgiving. You might not get quite the result you're after if you're careless, but short of extreme heat or hard radiation, it's quite difficult to completely kill a starter.
Unbleached All Purpose Flour
Water. Any drinkable water will do.
A container that's easy to clean. I prefer a pair of glass storage bowls, but often use inexpensive plastic storage containers.
A second container. You'll be washing quite a few containers, so it's nice to have two of them.
Rye Flour.
Rye flour has a slightly different blend of microorganisms that helps things along in the early stages. I almost always have some around, so use it, but I've not noticed any great difference in the end result if I start with white flour.
Pineapple Juice.
Adding pineapple in the first few days of the process lowers the pH and adds a bit of sugar, which moves the process along a couple of days faster. Specifically the stage you rush over is one where the "good" bacteria are Rather stinky. You'll be tempted to toss the starter at that point, so pineapple juice saves a bit of heartache. There's an excellent and thorough write-up over on The Fresh Loaf.
A scale
I use a scale and bake by "Bakers Percentage." However when the quantities are small—my scale isn't much use below 5g—I'll use volume measure as "Good Enough."
There are MANY methods to start a starter. This is the one I prefer, as it's spot-on reliable and doesn't require massive resources. If you find one that works better for you, I won't be offended if you use it.
In a clean bowl combine:
2 Tablespoons flour
2 Tablespoons pineapple juice or water.
Leave covered, but not sealed, in a warm place
For this stage I prefer whole rye flour and pineapple juice, but unbleached AP flour works just as well, as does Whole Wheat flour.
Add:
2 Tablespoons flour
2 Tablespoons pineapple juice or water.
Leave covered, but not sealed, in a warm place
At this point you might see some bubbling. If you're using straight water it might also start smelling icky. This is expected and okay.
Add:
2 Tablespoons flour
2 tablespoons pineapple juice or water
Leave covered, but not sealed, in a warm place.
By day 4 or 5, depending on how warm it is, your culture should be doubling overnight and should smell yeasty. It might take another day or so. Be patient!
At this point, it's time to figure out what kind of starter you want. Most of the time I only maintain a white starter, so at this point I'd switch to all white flour. If I need a wheat or rye starter, it's simple enough to create a fresh one, either from scratch or with a dose of my "normal" starter.
Combine:
40g of the starter
20g of flour
20g water.
Discard the rest of the starter.
Discard?
Well you Could toss it in a pan with a bit of butter and fry it like a pancake, which is YUMMY!
Yep. Feed your starter every day and it will probably live forever.
I keep mine in the fridge and feed weekly. When I'm baking, I'll pull it out Thursday and feed it to double size twice, which usually gives me enough for a bake.
What seems to work best is doubling it over several days, rather than all at once, but you can Try anything. If your starter is healthy and bubbling it will be happy as billions of microscopic plants can be in a big blob of flour, though your bulk (first) ferment may take longer. So long as you're adding equal parts by weight flour and water at each doubling it will work.
Take a look at my discussion of Leavening Equivalents. With this kind of "wet" starter, unless I'm told to do otherwise, I use 200g of starter in place of 100g of flour and 100g of water. If you have a sourdough recipe you're following, use the amount of starter specified in the recipe. Before you delve into the intricacies of Period sourdough research, I recommend you get your feet wet with some of the recipes here.
Sourdough.com has lots of lessons and recipes for budding sourdough bakers
True Sourdough more recipes, you might like their approach better, or perhaps not. It's all Yummy.