Measure out salt into a small bowl, using a ratio of 1 tablespoon salt per pound of cabbage. For example, for 3 1/2 pounds of cabbage, use 3 1/2 tablespoons salt.
Remove any damaged outer leaves from the cabbage and quarter it. Cut away the core from all four quarters. Finely shred the leaves with a large knife or mandoline. Place one-quarter of the shredded cabbage in a large bowl. Firmly massage one-quarter of the salt into the cabbage in a large bowl. Repeat this process until all of the cabbage and salt have been combined in the bowl. Add the caraway seeds if using.
Set the bowl aside for 30 minutes to allow the salt to begin drawing the water out of the cabbage. Using your hands, squeeze the shredded cabbage over the bowl, allowing the liquid to fall into the bowl. Pack the cabbage into a half-gallon jar. Use a wooden spoon or other tool to tightly tamp it down and remove air bubbles.
After all the cabbage has been packed into the jar, add the collected liquid. The cabbage should be covered by the liquid. Place a glass weight on top of the cabbage to keep in submerged. Cover with the lid and insert in the airlock into the lid. Set aside out of direct sunlight in a room between 65 and 75°F.
Check the sauerkraut daily to make sure the cabbage remains submerged in the brine. You will see small bubbles begin to form and collect on the surface of the brine. If there is any scum (white, yellow, or bluish growth), carefully scoop it off without stirring it into the liquid, and discard. The brine will take on a darker color over time, and the odor may be pungent.
When it is no longer bubbling, the fermentation is complete. This process can take anywhere from 1 to 2 weeks, depending on the temperature of the environment. Once the sauerkraut is finished, store it in the refrigerator, dividing into smaller jars if desired. It will last for several months.