As for that loaf up there, the only ingredients are flour, water, and salt. The "rise" comes from my own yeast and has a uniquely sweet and sour taste. The whole process is very satisfying, in the way that the whole process works in conjunction with nature but comes directly out of the kitchen.
Here is my process, which I have culminated from many sources, and developed my own way, but is perhaps most similar to Tartine's process.
Collecting Wild Yeast:
Helpful tools: A kitchen scale, a clean bowl (I use a pint plastic container, but glass would be fine)
Ingredients needed: The best quality flours you can get (I use a mix of Bread Flour, Unbleached Whole Wheat AP, and regular AP)
Day 1: Mix an equal amount of whole wheat and bread flour with water. I do this on a kitchen scale and have it come to about 120 grams. Mix it well with a wooden spoon or your hands and it should be a thin consistency but a thick batter. Keep it covered with plastic wrap and let it sit at room temperature for 3 days.
Day 3: Check your flour and water mixture for any activity. If there is a pool of water sitting on top of the flour mixture, dump or scoop some off and mix the flour and water together. You want to see small bubbles forming. If none have formed, let it sit longer for a day or two more until you see bubbles or some activity. It may be starting to smell sour at this point, which is a good sign.
Day 5: Bubbles should be beginning to form and it should be smelling sweeter, like very ripe fruit and sugar. At this point, the starter is active. If it is not, let it sit for a couple more days until it is.
At this point, the fermented mixture contains yeasts and is ready to begin being "fed" regularly on a somewhat daily basis. To feed it, discard much of the starter (a bit more than half) and mix in equal proportion of water and flour (1/3 Whole wheat, 1/3 AP, 1/3 Bread flour) until it measures 120 g on a kitchen scale . If it is a little more or a little less it does not really matter. What does matter is that the starter begins to bubble after feeding (it may take a couple hours), which means the yeast is active and feeding. Repeat this process everyday or every other day (just make sure not to skip very long periods, and make sure to check that the yeast is active after feeding) After a week of successful feedings, the starter mixture can be used in applications for baking where you would use other types of store-bought yeast. It is as simple as that, and makes a very big difference.