1. Don't wash your cabbage or radishes unless they have visible soil on them. Add all ingredients to a large bowl and salt thoroughly. Add cayenne now if desired.
2. Cover and let sit until the cabbage looks wilted and some liquid has pooled at the bottom of the bowl. Press firmly into a large, clean glass jar or several smaller ones.
3. Push the shreds down until enough liquid seeps out to cover everything well. If you feel you cannot get anymore liquid out but need more, add some clean, salted water. Don't fill the jars too tightly because gasses will form, the mass will expand and the liquid might be pressured out of the jar and end up on your counter!
4. Check for mold every once in a while and skim it off if any forms. Also taste-test every once in a while to see how sour you like it. I start to like mine once it hits the 1 week mark, but I keep it at around 71 degrees Fahrenheit. The hotter, the faster it will ferment.
The cayenne, ginger, garlic version more resembles Kimchi. The plain cabbage resembles sauerkraut. If you are going for traditional, you can add juniper berries, caraway seeds, and apple shreds to the cabbage.
I like to make mine with cayenne, ginger, and garlic because it inhibits mold forming at the surface. The mold shouldn't be harmful, but watch out for large amounts or brightly colored mold, those could be bad signs. In those cases, toss the affected jar.
If you have a good batch, you can use leftover juices to "inoculate" a new batch. This also causes the new batch to ferment faster.
Once you have this technique down, I challenge you to try this with different veggies. Cabbage and radishes are exceptionally easy to ferment, but almost any veggie will work. Try it!