https://www.thekitchn.com/how-to-make-homemade-sauerkraut-in-a-mason-jar-193124
Ive used this method a half dozen times over the years and has been pretty predictable.
Basic recipe is shred cabbage
Sprinkle 1 -1 tbs of salt on the cabbage in a large bowl, mix and let sit
After awhile, the cabbage wilts, and liquid forms at the bottom
Place cabbage and liquid in jar.
The recipe makes it seem like there will be enough liquid to cover the cabbage, but there never is.
The cabbage absolutely must be covered with liquid throughout the whole process , so they suggest if there is not enough water, mix 1 tsp of salt with one cup of water, mix and add to cabbage until it is covered .
I usually make a few cups of this 1:1 salt/ water solution, cause as I taste the sauerkraut through the process, the water level shrinks, so I just add a little more salt water to cover everything up.
Usually takes about 3 days to notice the fermentation process, but about 5 - 7 before it tastes like sauerkraut.
Definitely ferments quicker in warmer temps than cooler ones.
Basically leave on counter until you're happy with the result, then fridge or sometimes , I take a bunch, squeeze the liquid out, toss it in a ziplock and freeze ( My local pickle store lady told me that sauerkraut could be frozen, and sure enough it worked ).
I didn't so the caraway seeds, just cabbage, water , salt.