Chop cabbage into 1" (2 cm) pieces and add to a clean quart-sized (or larger) glass jar or other fermentation vessel.
Slice onions or split leek lengthwise. Add to jar/vessel.
Remove beet tops (greens), then wash and peel beets. If using organic beets, you can leave the skins on for a more "earthy" flavor.
Chop beets in to 1/2"/ 1cm cubes or slices. Add beets to jar/vessel (add them LAST if using other ingredients-- they are the heaviest and will weigh down the lighter veggies.)
Make brine (it's a 2% brine by weight): In a separate container, add salt to water and stir until salt dissolved.
Add sauerkraut or pickle juice to "backslop" and add good bacteria
Slowly fill the jar with brine.
If using jar, cover with a tea towel and place a rubber band around jar (to keep out flies and dust).
If using fermentation airlock device, follow instructions to secure/tighten it.
Ferment in a cool dark place (out of direct sunlight) for 14 days.
After 14 days, strain juice into another container. You can also use the beets for another purpose such as vegetable stock or a second run (see below).
Strain liquid into a glass bottle that has a tight-fitting lid (swing-top bottle or recycled mineral water bottle with a metal cap). Store in refrigerator, or start a secondary fermentation to mix additional flavors and create carbonation.