Chop the cabbage thinly with a knife, grate, or shave with a mandoline.
Add the cabbage to a large bowl or food-safe plastic tub. Toss to coat. Sprinkle with salt as you do so.
Add the cabbage to your crock or bucket one handful at a time, pressing it down firmly with your fist after each addition. Pressing helps pack the cabbage tightly, and forces water out.
Place the weights inside of the crock. If using a bucket, place the plate and the gallon jug of water on top. Cover the crock with its lid. Cover with a bucket, and secure with a towel or cheesecloth. Press down on your weights every couple of hours to help draw out water from the cabbage. Do this until the water level has risen above the cabbage. This can take up to 24 hours. If after 24 hours, the water level is not above the cabbage, add salted water with a ratio of 1 tablespoon to 1 cup of water to the container until it rises above the cabbage. Cover your vessel. Place the crock somewhere in your home where you won't forget about it. You'll be checking on it every day or so. Do not worry if you notice any mold; this is simply a bloom. The salty brine protects the sauerkraut. Skim off what you can and cover the vessel back up.
After about 4 to 5 days, start tasting the sauerkraut for flavor and texture. The flavor gets better and stronger over time. If your vessel is stored in a cool room, your sauerkraut will mature at a much slower rate than if it is stored in a warm environment.