Okay, so the lady finished up a big thing with her work, so I am currently hammered, working this lil party's music while she and others are more intoxicated. However, I will try to accurately describe below the process for making kimchi.
Firstly, most of it is super easy. What I'm describing here is not 'traditional,' in that the full cabbage is not being pickled. Instead, what's being described here is 'mak kimchi,' meaning we're cutting it into bite-sized pieces to allow for quicker fermentation and easier consumption once the stuff is done. While easy, you'll need some specialized ingredients:
The hardest of these to find, depending on your location, will be gochujaru. The most common brands come in large sealed packages, are relatively cheap, and should look something like this:

I have yet to find a perfect substitute for this stuff if it's not available. Depending on how many korean grocery stores are in your neighbourhood, you may have to venture to a specialty Asian restaurant supplier, and ask for 'korean hot pepper powder'. If you're in a relatively rural area, and really in a bind,
do not use chili powder or cayenne. Shit's different, and will mess up your kimchi something awful. Gochujaru is almost like smoked paprika. I would suggest aleppo pepper if you're really in a bind.
In terms of fi*sh sauce, anything will do, really, but I've found this stuff to be the the most readily available at Korean convenience places, and also the best in terms of taste and amount of salt:

Despite it's being 'squid brand,' it's actually anchovy-baed, which it recommended by most websites, and backed by Korean dudes I know.
If you do find yourself at a korean grocery, it's worth your time to find shrimp sauce as well. It'll be a paste made of tiny tiny shrimps, resembling this:

Don't be duped by similar-looking jars of dried shrimps. These should be a wet paste that's salty and near-mush. Don't worry, there will not be 'entire shrimps' in the finished product.
With those caveats out of the way, you'll need to assemble all these things:
2 or 3 nappa cabbages, depending on size.
a carrot
a bunch of green onion
1 daikon (pretty much optional, but helps. Regular radish can be easily substituted)
The aforementioned Gochujaru pepper
3 cloves of garlic
a 1-inch cube of ginger
some f*ish sauce (preferably anchovy-based, from a korean grocer, but the difference if not is negligible)
1 Onion
1/2 cup of cooked rice (preferably sticky rice, it's no big issue of you use other stuff)
1/2 a pear or apple (again, optional. Pear is better).
4 or 5 fresh oysters &/or 2 heaping tablespoons of shrimp paste (optional, but makes a positive difference)
sea salt (or kosher salt. No iodine is preferable)
Soaking the cabbage is the weirdest step. Cut off the tough bottom of the nappas, and chuck these away. After this, cut up the cabbage into large, rough pieces. Some pieces will be all white stalk, and some will be mostly leaves. This is all normal. Place this cabbage in salted water, roughly a 1-10 salt-water ratio. Making this exact is not crucial. Put your cabbage into a big mixing bowl, and pour the water on, making sure the cabbage remains submerged under the water. If some of the cabbage sticks out and remains exposed to air, stick a heavy object on top of your cabbage-piece mountain to ensure it all stays entirely submerged in the brine. Leave it in there for at least 3-4 hours, stirring it around at least a couple times throughout to ensure even brining. Overnight works too. Should look similar to this:
While this is going on, you get to make the paste: now this shit is more of an art than a science, hence the lack of exact measurements. Take around 3/4 cup of f*ish sauce with a cut up onion, your rice, the garlic and ginger, seafood, and the half pear or apple, and blend all these until they are a paste. If adding fresh oysters—which is totally recommended, and greatly enhances and 'complexifies' the flavour—shuck them at this stage, and just toss them in raw. Don't worry, you will not die, nor will you kill anybody. Put the resultant bright red slop into a bowl. After this, use a carrot peeler to make thin strips of the carrot, cut the daikon into matchstick-sized pieces, and put these directly into your paste mixture. Same with the green onion, chopped into roughly inch-long segments. Mix these into the sauce. And now, you have your basic kimchi paste. Have a gander:

Now, once your salting period is elapsed, your cabbage should be noticeably shrunken, maybe kinda withered. Drain the brine, and wash the cabbage pieces off under the tap for quite awhile to ensure the end product doesn't have a whole lotta salt on the outside.
Now, you just toss the two—your salted cabbage and your paste—together. Pack your kimchi into some tupperware or another airtight container. No real need to sterilize. Be sure, however, to push the stuff down to fit the maximum amount in your given vessel. Eliminate any air bubbles where possible. YOU NEED TO LEAVE AT LEAST THREE INCHES OF AIR IN YOUR GIVEN CONTAINER, though. Otherwise, shit will explode. It will not be nice.
Leave your packed-up kimchi in its container(s) at room temperature for around 24 hours, then put that shit in the fridge. Leave it there for two or three weeks. Open it up every other day, though, and let the gasses out.
Over this amount of time, you will notice that more liquid will form in your kimchi. This is good. Keep pushing the kimchi down to ensure the cabbage itself is under the liquid. This ensures that no nasty moulds will form, and that the lactobacillus bacteria will do their work.
After around two weeks, try the stuff. It should be sour and slightly effervescent, with none of the individual ingredients being noticeable or overwhelming. Instead, it should have an intense umami flavour with a lot of saltiness and some sourness. It should taste divine. If you can eat it on its own, you've done well. Shit should look something like this, likely with more red liquid:
N.B. that it will smell BAD. However, once you've first tried a good well-fermented batch of kimchi, you'll not notice the scent. Instead, it will signal to you that your precious beautiful batch of cabbage is ready to eat and be enjoyed. Another relatively important thing to do when you're in the process of eating/using the stuff, is pack it down under the liquid when you're done eating it. It'll store in the fridge for months, maturing and getting better with time, but you risk allowing weird moulds and mildews to form if you leave too much of the finished product exposed to air inside the container. keep the stuff tightly packed, and the liquid which comes with proper fermentation will do the job is keeping it unexposed to air, and the nasty free-floating yeasts and moulds therein.
Sorry for the huge puke of words, but it's a food I really feel passionately about, and even super-old kimchi is excellent (even recommended) for use in soups and other korean recipes. If you try this and are successful, please hit me up for more. I'll gladly talk for way too long on the subject.
[edits involved more pictures, greater ingredient specificity, and a decrease in the length of salting time. Some websites say and hour and a half is fine, but batches of experience tell me to do no less than three hours. Five or more is optimal. It'll be soggy-looking and stinky in the bowl, but the increased time will result in crunchier 'chi in the long term.]