Twenty-four hours before you plan to start your bread (i.e. 39-45 hours before you want to pull the bread out of the oven—see note below on timing), you need to “refresh” your desem by feeding it warm (80f) water and flour.
Break open the starter ball (also called the “chef”) and scoop out the insides. Add about 3 tablespoons warm water to the crumbled starter. Stir with your fingers to dissolve it. It will feel like a goopy batter. Now add some of the flour from the starter container and stir with your fingers, just until the starter becomes a dough and starts to come cleanly away from the sides of the bowl. It will be rather moist and sticky. Cover and ferment at room temperature for about 12 hours. Discard the “rind.”
At the end of 12 hours, refresh it again, exactly as before, with another 3 tablespoons warm water and more flour. Let ferment another 11 or 12 hours. Your starter (now called a “levain”), will now be ready to use.
After measuring/weighing out the desired amount of starter for your recipe, you need to make a new starter ball. Weigh 4.5 oz of the levain and knead in enough flour (again from the container) to make a rather stiff dough. (You don't add any water this time.) Form into a ball and put it back in its container. You will have had to mill some more “surrounding flour” to replenish the amount you used in the refreshments and recreating the starter ball. Refrigerate until next time. (Contrary to what Laurel's Kitchen says, you can let the starter sit for weeks in your fridge without feeding it, as long as you wake it up with those two 12-hour refreshments.)
A note about timing: Making bread this way seems complicated at first, but that's only because the directions have a lot of words! The real necessity is time, and the only other complication is the logistics. The actual active-making-bread time is very minimal. The best way I've found to organize my bread-baking is to feed the desem initially in the evening. If you do that, your schedule looks something like this:
Monday 8pm: feed desem.
Tuesday 8am: feed desem.
Tuesday 8pm: start bread; put new desem chef in the fridge for later use.
Wednesday between 8am and 2pm: round loaves, set them to proof in pans.
An hour and a half later: put bread in oven to bake.
Forty-five minutes later (Wednesday between 10:30 am and 4:30 pm): bread is finished! :)