There are many types of kimchi eaten in Korea. Baechu kimchi, the most common variety, is made with Chinese cabbage. To make a batch of baechu kimchi:
5 heads of Chinese cabbage
2-3 heads of garlic
3 cups of salt
2 cups of red pepper powder [see below]
1-2 knobs of ginger
optional: chopped scallions or watercress, cubed daikon radish
Red pepper powder (kochukaru in Korean), a coarse powder of chili pepper flakes, can be found in any store selling Korean foodstuffs. It is made from a pepper of medium heat. If using a hotter pepper, use less (but kimchi is supposed to be spicy)!

Wash the Chinese cabbage well, remove the outermost leaves and trim off the root. Traditionally, the heads are split lengthwise, and made into kimchi in this form. I recommend cutting the cabbage into smaller pieces, as follows: After splitting lengthwise, cut out a bit of the solid mass near the root. Laying halves flat side down, make 3 lengthwise cuts along each half. Then chop widthwise into one inch wide sections.

Place the chopped cabbage into a large bowl or basin. Take 2 cups of the salt and make a brine with 15 or so cups of water. Pour the saltwater over the cabbage, and mix well. Let this stand for at least one hour.

Chop up garlic and ginger. The amount you use is up to you. I never use exact amounts...and I've always enjoyed the result, even if it sometimes comes out more gingery or garlicy or spicy than usual.The only thing you really need to make kimchi is the salt: since this is a raw food, a certain amount of salt is needed to pickle and preserve the cabbage.

Mix the garlic, ginger, 1.5 or so cups of red pepper and the remaining 1 cup of salt with a half cup or so of water. Mix it well. Your mixing hand will start to tingle. Relish this sensation.

Once the cabbage has soaked for an hour in brine, drain off all of the liquid, then rinse the cabbage and drain again well.Mix the paste from above into the cabbage. Add optional ingredients mentioned above, if desired. Mix it all up well, until the paste coats the cabbage evenly.Mix it up some more!

Once it's thoroughly mixed, place the mixture into very clean containers. Fill containers close to the rim.If there is some red liquid left over, pour it into each container. You don't want any air pockets in the kimchi containers, and you do want the cabbage to soak in this kimchi juice.

Clean off the lips of the containers, and put on lids. Do NOT tighten lids too hard. Let the containers sit at room temperature for 2-3 days, and as they begin to ferment, air will bubble out and containers may leak a bit.Traditionally, kimchi is put into ceramic crocks and buried in the earth. You can put yours in the fridge. At fridge temperature, it will continue to slowly pickle, getting more tangy with time.You did it! You made your own kimchi! Enjoy.

Other Kimchi variety...
Kimchi Pancake: http://chowhound.chow.com/topics/530450
Kimchi Fried Rice: http://www.maangchi.com/recipes/kimchi-bokkeumbap