My basic recipe (makes about 3/4 gallon, to fit into a 1 gallon jar):
5 lbs. cabbage (one huge, or two medium cabbages) (can use some carrots, beets, etc. instead of all cabbage)
3 tbsp. salt
Shred the cabbage or thinly slice, reserving a few outer leaves.
Mix salt and cabbage together in a large bowl, mixing thoroughly; taste to see if you need more salt. (If you have chopped the cabbage into larger pieces, you can let the cabbage and salt sit out at room temperature, stirring occasionally, for about 4-6 hours, until the cabbage starts to give up its water.) The unfermented kraut-to-be should taste salty, like a good soup.
If you like, you can pound the cabbage with a wooden spoon, kraut pounder, or hardwood children's building block, to get juicier kraut. Sometimes I'll leave the bowl of kraut out for the afternoon, pounding a few times whenever I walk by.
Put cabbage mixture into a glass gallon jar, shoving it all tightly inside. The liquid will start to exude from the cabbage; keep shoving, so that you end up with all this juicy cabbage tightly packed into the bottom of the jar.
Carefully pack the whole outer cabbage leaves on top of the shredded stuff, rolling up one or two leaves to keep everything down. You want the kraut to be fully submerged in its exuded liquid while it ferments (unless you use “bail clamp” canning jars (Fido is a good, fairly inexpensive brand that can be found in many supermarkets’ canning section) or similar airlock, in which case it doesn't matter. Basically, it is easiest if the lid can _slightly_ deform as the kraut ferments, which will allow higher-pressure gasses to escape from inside but then don’t allow oxygen back in again. Bail-clamp lids on your jars make fermenting much more foolproof! Second best are plastic lids on glass bottles, screwed on very tightly. Not great but do-able are metal lids on glass jars – it is too easy to tighten them too much...so that when the gasses escape, your glass jar breaks. :(
Place the jar on a plate to ferment at room temperature. This goes quicker in warm weather, but I like to keep it going for at least two weeks, ideally 4-8.
I never open my ferments while they’re fermenting. The basic idea is that oxygen has to be mostly excluded from the ferment, either because the vegetables are covered with liquid, or because of an airlock-type or similar tightly-fitting lid.
Four weeks or so later: enjoy!! :)
A NOTE CONCERNING CULTURING OTHER KINDS OF VEGETABLES:
Pickling is a variation on the kraut process, a technique used to ferment veggies (like carrots or beets or radishes or...) that do not exude as much liquid as cabbage does.
Basically, if a vegetable is less juicy, or you do not want to pound it (for example, to make carrot stick or radish slice pickles), you can wash, chop, and pack the veggies into jars, and add salt water (3 tbsp. salt per quart of filtered water) to submerge the veggies. Then, ferment on the counter. Some vegetables, like cucumbers, go very quickly (pickles are usually done in three to five days..
Sometimes I will use half cabbage to inoculate the pickles with the Good Bugs found naturally in abundance on cabbage leaves.
If I want to make dilled carrots, or plain beets, or anything similarly cabbage-free, I use Caldwell's Cultured Vegetable Starter. This always prevents mold, in my experience, and the pickles come out fantastically.