The photo on the right is not cabbage with feta; it's mold. If exposed to too much oxygen, the proto-sauerkraut will get all scummy since fermentation is an anaerobic process. Make sure to seal mason jars tightly and if using a crock, place a plate or cloth—or a cloth tied with a rubberband, to avoid flies—on top. Submerge the cabbage in lots of salty water, and smoosh down at least once daily to release air. As Boing Boing points out, it's pretty easy, despite the mold threat.
A good fermenting takes at least three weeks, and for an especially potent flavor, wait around six to nine months. For more on the magical ways of fermentation (including beer, yogurt, wine, mead, and miso), read Wild Fermentation by Sandor Ellix Katz or "Sandorkraut," who has spent almost two decades fermenting for fun. He doesn't stress about mold. Just skim the stuff off, and place the top back on.