First let me discuss the fine print. I have never tried this. This comes from conversations with one of my relatives and it sounds rather plausible. So, if anyone has tried this, please let us know.
The basic theory is that you can take a growing grapevine and simply redirect it back into the ground and back up. You bury the end of the vine four to six inches in the ground. Bend it into a U shape so the end of the vine protrudes back up out of the ground. That end then becomes a new grapevine with its own roots.
The basic concept is the same as using cuttings to grow new grapevines, but you do not have to cut them, or wait until next spring to plant them. You can do this in the middle of the summer, any time you have a cane long enough to reach the spot you want to start a new grapevine. The draw back to this is you have to start the new grapevine pretty close to the original. However, if you happen to have an unruly grapevine that you are planning to begin to use, you probably have several very long canes. You could start several new grapevines and start a mini grape vineyard.