I just use salt for the actual lactofermentation process (you can season with other things). The ratio is 3 tablespoons of non-iodized salt per five pounds of vegetables. Chop the vegetables (the smaller the veggie pieces = greater surface area = quicker culturing), add in the appropriate amount of salt, and massage the salt into the vegetables until they begin to release water. If they get really juicy right away, I jar them up, and if not, I let them sit for a little while til they start sweating (half an hour to overnight, depending). To pack them into jars, add small amounts at a time to a clean jar and press it in very firmly. Once all the veggie pieces are in, pour in the remaining liquid, which should cover the top of the packed veggie pieces. If it doesn’t, you can make some extra brine to cover at a ratio of 1 tbsp non-iodized salt per 1 cup of water. You can either put the jar’s lid on or secure a cloth over the top of the jar with a rubberband. If you use the jar lid, you’ll need to “burp” the jar every 6-12 hours until you refrigerate it, which should be after a few days at room temperature. You’ll start to see bubbles forming between the vegetables, and some veggies change color slightly (but uniformly, and there shouldn’t be any bad smells).
You can’t pickle ALL vegetables this way, but pretty much anything that’s sturdy works: cabbage, brussels sprouts, turnips, beets, carrots, onions, garlic, radishes, celery root, asparagus, parsnips, ginger. I’ve even included some mustard greens in a batch of napa cabbage kim chi before, and it worked well.
I’ve heard that the Body Ecology Diet advocates lactofermentation without salt, using specific “pickling spices.” These have a shorter shelf-life but are supposed to be advantageous in other ways. I’m not well-versed in it, so I can’t really comment. A friend brought me some a year or so ago, and it was definitely flavorful.
I hope my wordy recipe format is still helpful.
edit: I’ve only ever used vinegar for pickling when I specifically wanted “vinegar pickles,” because they taste more similar to the Vlasic yellow-dyed crap I grew up with and still secretly love. I made some really tasty dill vinegar-pickled radishes last year. Vinegar pickling is useful in that it preserves a lot of nutritional content, but since I used distilled vinegar, it’s not contributing to the health of my gut flora to eat them at this time. I guess they’ll be waiting for me.