The primary variables that a home sauerkraut maker can control are; air, salt and water. The secondary variables are temperature and light. Here is some information I have collected from the web.
The lacto fermentation process is anerobic; that is, you do not want oxygen in the air to have access to the cabbage. The primary barrier is simply to submerge the cabbage in a brine (salt water) solution. This has been used for centuries. Traditionally the cabbage, salt, and water are placed in a crock. A weighted plate or other disc is used to keep the cabbage submerged. A cloth or other barrier is used over the crock to reduce air, insect, and possibly rodent access to the fermenting sauerkraut.
The modern home sauerkraut maker has several approaches for lower risk production of small volumes. The first is to use a mason jar as the fermenting vessel. One average cabbage will be enough to fill one 2 quart mason jar. This is a very nice batch size to use to experiment. You can also use any similar container like a large empty mayonnaise jar.
The traditional cloth over the crock is a poor barrier for undesirable items entering the fermentation vessel. If you seal the mason jar tightly you risk that the carbon dioxide from the fermentation process can develop sufficient pressure to explode the jar. I do not personally know of anyone that has exploded a mason jar, but a friend has exploded a few wine bottles making kombucha. Messy at best, dangerous at worst.
My suggestion is to use an air-lock system, a wine makers bubbler, to allow carbon dioxide to vent from the fermentation vessel without allowing air to enter. One company, pickl-it.com , sells a complete system of this type. You can make a very similar system by purchasing the components from a local home brew or wine making supply store.
The salt you use should be pickling salt, kosher salt, or sea salt. The important thing is to avoid salt with iodine or other additives that might discolor the fermented sauerkraut.
Finally the water. Tap water contains chlorine or chlorine compounds to prevent bacterial growth. For home made sauerkraut we want to encourage the lacto bacteria to grow. In most cabbage fermentation you will not need to add much water. When you do add water it is best to use carbon filtered water, well water, or water from other sources that that does not contain chlorine or chlorine compounds.
The best fermenting temperature is cool room temperature. Direct sunlight should be avoided since light in the ultra violet spectrum is antibacterial. The traditional fermenting location is a basement.
Next: A recipe and my results