Wash the cabbage. Discard any wilted outer leaves of the cabbage. Cut the cabbage in quarters and remove the core. Cut the quartered wedges in half, lengthwise creating 8 wedges. Cut thin ribbon-like strips across these wedges.
Wash and shred your carrots.
Transfer the shredded cabbage and carrots into a large bowl. Add salt and using your hands, squeeze the juices by massaging the cabbage and carrots together. This should take about 5-7 minutes before juices start flowing easily. You don't want to overdo it as the sauerkraut will turn into one big mushy mess. There should still be a crunch to it. If you desire to add any spices, like ginger or caraway seeds add them towards the end of this process.
Pack the cabbage and carrots into a clean jar. It's easiest if you have a wide mouth canning funnel but your good ol' hands will work just fine. Pack it nice and tight. Every so often, pounding the cabbage/carrot mixture with your fist to allow the juices to rise to the top. Leave about 1" from the top for
Place an outer cabbage leaf on top to make sure the sauerkraut stays submerged in its juices. Weigh it down with a clean, sanitized clean rock*.
Place a doubled cheesecloth or thin fabric over the mouth of the jar and wrap a rubber-band around it.
Set it in a cool, dark place for 3-7 days, checking daily for taste and pushing the sauerkraut down as the liquid will be rising up.
The sauerkraut is ready when you think it's ready, usually after 3 days at room temperature (65-75F). There's no set rule for when it's "done". You can continue to let it ferment on the counter, provided that it be kept away from sunlight and that will produce a more tangy taste. After it's stint on the counter, put a lid on it and transfer to cold storage. Keeps in the refrigerator for up to a year.