My paternal grandfather was born in south-central Pennsylvania of straight-up Pennsylvania German stock, and from him I inherited both my surname and my native cuisine. As a teen I helped him and my father make sauerkraut, which was made according to the following method:
You will need:
1. Fresh heads of cabbage.
2. Several pounds of salt.
3. A five-gallon earthenware crock.
4. A kraut stomper.
5. A good-sized (say, grapefruit-sized) rock.
6. A dinner plate.
7. A cotton cloth big enough to cover the top of the crock.
8. A cabbage slicer (alternately, a large knife and cutting board).
A kraut stomper is the long wooden implement on the left. The cabbage slicer is the rectangular doodad on the right:
The sauerkraut is prepared as follows:
Shred the cabbage by slicing the heads into slices 1/8th of an inch (3mm) wide, more or less. The slices will fall apart by themselves into piles of shredded cabbage. Layer the shredded cabbage in the crock. When it's about an inch deep, shake a goodly amount (two handfuls) of salt over the cabbage, and start crushing the cabbage with the stomper. You want to use enough force to bruise the shreds and bring out the juice. When you start to see froth forming as you work, you know you are doing it right.
Continue adding layers of cabbage and salt, stomping as you go. You will know that the amount of salt is right if you taste it and the salinity reminds you of seawater... it should be that salty. The stomping process will mix the cabbage; this is fine, it's part of the process.
When the crock is full or you've run out of cabbage (whichever comes first), move the crock to a cool, dark location. Lay the dinner plate on top of the cabbage (yes, right in the juice) and put the rock on the plate. Drape the cloth over the whole affair and leave it alone for six weeks to two months.
After the fermentation is complete, remove the cloth cover, the plate, and the rock. The top layer of sauerkraut may be discolored due to any number of reasons, usually due to drying. Sometimes mold may form on the top of the kraut. Do not be concerned about this, but simply skim the top layer away with a large spoon and discard it. It's of no more import than mold on the rind of a cheese.
The remainder is genuine home-made sauerkraut, suitable for serving with roast pork and mashed potatoes, or topping a bratwurst in a bun. It may be home-canned or frozen, and keeps very well either way... or you can just store it in the crock there in the basement, where the natural lactic acid will continue to act as a preservative. We preferred to freeze ours.
-der maus
Ridiculous that people would disregard such good info because of his sexual orientation. 
Fermented foods have always been a part of my family's diet. We've never used vinegar for cucumbers.
