It is not impossible to produce kefir grains from scratch, but it is impractical for most. I have done it myself, but it took about a month of changing milk 3 times per day and 6 gal of milk in order to get grains no bigger than peppercorns. But it is possible. I'm growing them larger now.

There are research papers on the science behind kefir grains, but I won't bore you with the details. The short story is the grains are always being formed, but they are microscopic and take a long time to grow to the point that they can be collected without lab equipment.

This is my abridged procedure.

Start with a sample of good quality kefir. I think best to use kefir made from grains since it has a better mix of bacteria and already has a know history of growing grains. Note: The best paper on creating grains used dry kefir culture instead of kefir from grains so that also works.

Heat pasturize nonfat milk. I always do this because I don't want to risk introducing other bacteria. Refrigerate it. You'll use a gallon or more per week. Use only nonfat milk. Fat milk makes the kefir too thick and harder to separate grains.

Put a table spoon of kefir in a pint jar with 1 cup of milk. Mix. Leave the lid slightly loose to vent any generated gases.

Let stand at room temp until it just starts to separate. Do not shake or disturb. Pour off 2/3 to 3/4 of kefir into a quart jar without disturbing the bottom portion. Add 1 cup of milk to the pint jar.

Repeat the previous step 1 to 3 times per day for about 30 or 40 milk changes. The time depends on temperature so watch closely. If it cultures too long at one step and too many curds forms, no worries. But it will be time to move to the next step early.

At the last milk change allow the culture to go until it separates and forms curds.

Shake the kefir slightly to break up the mass and strain through a very fine mesh like a nut milk bag. All solids collected go back into the pint jar. Add a cup of milk and let set a room temp until it just starts to separate.

Repeat the previous step 1 to 3 times per day.

After another 30ish milk changes, start look in the strained solids for signs of translucent grains. At some point they will become large enough and numerous enough to start separating from the strained curds. At this point rinse the solids with distilled water and collect the grains from the other solids and place in a clean pint jar. Don't worry about removing all of the curd from the grains. Add 1/2 cup milk and let set for about 12 hours. It should not start to separate because of the smaller amount of culture material used. Strain and repeat. Adjust culture time to when culture just starts to separate. When it starts to separate in less than 8 to 12 hours, increase the milk from 1/2 cup to 1 cup. Continue until grains are big enough to make batches of kefir.

The kefir poured or stained off goes into a separate quart jar and is left out to culture longer until the jar is full, or the desired taste is acheived and then refrigerated for consumption.

Update: At the end of these steps I collected about 8 grams of grains, all smaller than peas, but enough to culture a pint of milk in 24 hours. They are growing at a little less than 10% by weight per day.

This was a great experiment and I'm glad I did it, but unless someone just enjoys trying things like this I suggest buying starter grains as most others have posted. The time and effort required to make kefir grains from scratch was not worth the trouble if it is just to save a few dollars.