I love to make sauerkraut and I wanted to share the "recipe" if you want to call it that, but I do have a couple tips.
First, start with the freshest cabbage you can find. They will yield more liquid which is critical to the process. Slice up the cabbage pretty thin, use a knife, mandolin or the slicer attachment on your food processor. Have Kosher salt nearby. Pick a container that you will be able to add a weight to. It would be ideal to have one of those awesome crocks made for fermenting, but sadly, I do not. I used two, round 5 qt containers. One to hold the kraut, the other to fill with water to weigh down the kraut.
Don't hesitate to add in onions or garlic if you would like to. Even the red cabbage makes a beautiful pink kraut.
Once you have all the cabbage thinly sliced you are going to layer cabbage and salt. The salt will help draw out the water as well as flavor. With each layer of cabbage I used a small amount of salt, maybe 1/8th teaspoon. After each layer, using your hand, mash down. Keep layering and mashing as much as you can.
When you get done, put your weight on top, it can be a plate with a large can of corn. Check it in an hour and see if more water has been expelled. If it looks like some has, give it another hour and check again. The liquid MUST cover the top of the cabbage. If after 3 hours it has not covered the top of the cabbage you need to boil some water, let it cool and add just enough to cover. If it seems like you need to add a lot of water (that means you had old cabbage) you should salt the water as well. It may seem like you've added a ton of salt, but it will not be over salted.
I placed mine in a dark area in the pantry. I check on it every few days to make sure the liquid is covering it and push it down a little more. I usually don't get any "scum" on top, but sometimes it happens. Just scrape it off and keep going. I let mine go about 6 weeks, but you can taste it after a couple of weeks and see what you think.
Once it's where I want it I put it in jars and in to the fridge. You can process it in a water bath if you want to keep it on the shelf, but I find this softens it too much and makes it more like store bought.