Wiki has a pretty good overview article on kimchee.
I make several kinds, but what's most often thought of in the West as kimchee-- i.e. the one served most often in Korean and Japanese restaurants and noodle joints-- is Baechu Kimchee, the one made with napa cabbage:
2 large heads of napa cabbage, chopped into roughly 2" squares
8 cups of water
1 cup coarse, non-idodized salt (kosher salt or pickling salt)
I medium bulb of garlic, finely chopped (try to get northern hardneck garlic for this, as the Chinese stuff isn't nearly 'hot' enough for good kimchee)
1 1/2"- 2" knob of fresh ginger, finely grated
Generous 1/2 cup of Korean kochukaru chlli flakes
1 bunch of green onions, coarsely chopped, OR 1 large cooking onion, sliced
Mix salt and water in a large, nonreactive bowl.
Add cabbage and weigh down with a plate on top of which you've placed a jar of water (to submerge all the cabbage in the brine).
Soak cabbage overnight.
The next morning, remove the cabbage and discard the brine.
Lightly rinse the cabbage, squeezing out excess water.
Clean your large bowl and add garlic, ginger, chilli flakes and onions.
Add the cabbage and toss to distribute the seasonings.
Pack the mixture into a large jar with a tight-fitting lid.
Allow the kimchee to ferment in a cool place for a week or so.
It will then be ready to use. Once you've opened the jar, it should be kept in the refigerator after that.
That's it! We really enjoy "living food" at our house-- kimchee, yoghurt, miso, sauerkraut and other stuff that contains active enzymes. When they interview us on our hundredth birthdays, we're going to attribute our longevity to having eaten them daily.