To make sourdough you will need a sourdough starter, which is essentially flour and water mixed and left to gather bacteria. Yes, sourdough is sour because of bacteria, which in turn eat away at the starter and produce waste (lactic acid). Yeast itself will produce alcohol when left to its own devices, which is why it is used to ferment things such as...well, alcohol. The bacteria eat that too, leaving behind what essentially amounts to vinegar. Neat.
Note: Thank you for the clarification, atomictesting. Fixed for correctness.
A fair warning before we get started: Completing this instructable can take anywhere from one week to several months, depending on the amount of time you are willing to spend and how many times you accidentally screw up.
I will not be using active-dry or rapid rise yeast at any point during this instructable at all.
Why wild yeast?
Why not? It's neat and, given the right about of time, your sourdough will take on its own distinct flour not quite like any other starter.
Why is it sour?
Bacteria and wild yeast. When you let the starter and the bread sit as long as you will be (days and weeks) it takes on that distinctive sour flavor.
How long does this take?
Forever. It's an ongoing process.
How much experience do you have?
Not a lot. I'm a hobbyist. I'm very open to suggestions or corrections if someone out there knows something that I don't know.