Real* kefir is made from kefir grains. These are not grains like wheat and rice--they're not really grains at all! But they look like grains. Actually they look more like a clump of cottage cheese. The grains themselves are some sort of crazy mixture of polysaccharide/bacteria/yeast thing. Don't ask me where it originally came from, but my understanding is this stuff (some of it? all of it?) has gotten passed on for generations.
When I made coconut kefir I would just stick the grains in some coconut milk and let it sit out, covered for 24 hours. Then I would remove the grains and put them in fresh milk all over again. The liquid that remains after removing the grains is the kefir. Drink it plain or add it to smoothies or put fruit in it or...consume it somehow. (You don't have to drink it right away though and you can store it in the refrigerator.)
Kefir is really easy to make, but you do have to take care of the grains. If making non-dairy kefir, like I was, the grains needs to be put in real milk every once in a while in order to keep them alive. They feed on the sugars in milk, so the coconut milk or other non-dairy milk will not feed them. They won't feed off of plain sugar, either--it's got to be milk sugars.
Source and for more information on kefir and how to care for kefir grains: Cultured Food Life.
*You can also make kefir from a packet of cultures like this, but it will not continue to reproduce indefinitely.