Sorry, been away from the computer. This is the most basic recipe I can come up with and it's intended for anyone to be able to do without special tools or supplies. You can get a whole lot fancier if you invest a bit of money into better stuff.

To do a basic sauerkraut, you need only five things:

-Cabbage

-Salt (kosher/picking salt works easiest but any will work. avoid salt with lithium and iodine as they prevent microbial growth)

-Water

-A fermenting container (no metal!) If you have some jars on hand, go grab them. If not, start collecting used pickle and mayonnaise jars until you have 4 - 5 around.

-A dark or covered place that remains at room temperature. If you have a tray, get that out to catch any drips.

-Optional flavors--mustard seed and caraway seed work well, so do black peppercorns. This is where you can get experimental. Add about a teaspoon per cabbage.

For understanding scale, a single cabbage will fill somewhere around 2 regular pickle jars. I like to keep more around just in case you need more space.

Take off outer leaves from your cabbage and save them. Cut the cabbage in half. Try to remove the thick core that will be near where the root came out. You should be able to cut out a triangular wedge and remove nearly all of it. A little bit doesn't matter--it's edible, but tougher than the rest. You will notice the texture difference but I have never found this to be a big deal.

Lay your cabbage half on a cutting board. With a sharp knife, make vertical cuts throughout trying to keep the size of each the same. It doesn't really matter how you cut it--this is your preference--but it should all be consistent for a consistent result.

If you want to get accurate, weigh your cut cabbage. For each 100g of cabbage, you will separately measure out 2g of salt. It doesn't matter what measure you use, your target is 2% salt by weight. If you don't have a scale, that's fine. For each cabbage, measure out a heaping tablespoon of salt.

Mix the sat very well throughout the cabbage. Massage it firmly with your hands for several minutes--you actually want to bruise it a bit. Let it sit for a while--perhaps as much as an hour--for the salt to draw out water. If enough water is drawn out, it will make its own brine. This seems to depend on each particular cabbage and sometimes it will be necessary to add in extra brine on top.

Place the cabbage in your jars and tamp it down. Use a large spoon or similar and push it with some force deep into the jar trying to fill in all the space possible. You need roughly 25% head space (i.e. leave the top 1/4 of the jar empty) to accommodate the release of CO2. The fermentation process will cause everything to expand and you don't want it pouring out of your jar.

At this point, let the sauerkraut rest for a few hours uncovered as it will continue to form more brine. I tend to do the steps up to this point in the morning and the following steps in the afternoon or the evening.

For each jar, take a cabbage leaf and use it as a cloth to hold the cabbage down below the brine layer. You can tuck it in around all sides of the jar. It is IMPERATIVE that very little of the cabbage be exposed to the air or it will rot rather than ferment.

If you need to create more 2% brine, then get out your scale and weigh out 200g of water. Add an additional 4g of salt and mix until dissolved. Pour into each jar as necessary until the cabbage is properly covered. If you don't have a scale, then you can put in about 1.25 tablespoons of salt per each two cups of water.

Cover the jars with their original lids. These lids should be left not only loose, but completely unscrewed. Take no chances of letting gas build up lest you explode a sauerkraut somewhere. If I ferment in a jar, I just put the lid on top of the jar and don't rotate it. Put jars in your fermenting location and cover with a cloth--this is mostly to keep direct light out but it can also keep dust and such out.

Allow the saurkraut to ferment for roughly 2 weeks. I like to open them every couple of days to give them a good sniff. If things are going well, it should smell bitter but not rotten--if you are like me, you'll unironically go "Hey it smells like the stuff in the store!". The liquid on top should also be generally clear but perhaps a bit cloudy. If you notice mold on top, then the salt balance may have been off. You can scoop off the top layer of liquid/mold and add in more brine, though if it is way off, you may not be able to correct it.

After 2 weeks, give it a taste/smell. Does it need more time? This is your call. If so, leave them out for another week. If not, throw it in the fridge and let them sit for a day. The following day, you can screw the tops on tightly.

I use a fermenting pot that you can get on Amazon:

https://www.amazon.com/dp/B09L94YNGX

This works better but I found that it also takes a bit more practice than the jars. The jars are your perfect place to start and at really minimal expense. I will note that I have had several batches fail for a number of reasons that I learned lessons from. Most of them have come out just fine, though.

I hope this works for you. Please let me know if you do some sauerkraut and send photos.

P.S. my favorite recipe is to use one green cabbage with one purple cabbage. Comes out sort of a bright purple color. Add in a teaspoon each of caraway and mustard seed per cabbage. Lots of flavor!