We learned all about double-digging from two sources: (1) the farmer, Josephine, we apprenticed with in Argentina and (2) John Seymour's book, "The Self-Sufficient Gardener." Both are invaluable to us, and fortunately, we can flip through the book anytime we have any how-to questions (I resist the temptation to just search for it on the internet).
Simply, double-digging involves digging into the earth two spade-lengths down. That's about two feet. In the process, you aerate and loosen the soil as you dig. Seymour recommends starting with the first row of your bed by removing the sod and then digging out the soil and placing it at the head of the bed exactly how you take it out. So the SW corner stays in the SW corner, etc. Once you've dug down 2 spade-lengths, then you fork (or in our clay/rock soil case, pick axe) the soil at the bottom to loosen it up. Place the sod back in the bottom of your row (it won't take root again since it's deprived of light), place the bottom soil on top of the sod, and the top soil back on top of the bottom soil. Meanwhile, mix in as much organic matter (e.g., manure, compost) as you want/can. You end up with a row of loose, aerated, organically-supplemented soil that is now raised up a few inches above the ground line. Continue along your bed, row by row, in this fashion.
The major pros of double-digging are to loosen the soil (i.e., aerate it so roots and earthworms can find their way through and to promote drainage) and to add organic matter to it. Because our land had not been cultivated for many years, it is in dire need of air and organic matter, so this is why we double-dig.
Some people recommend against double-digging because it is not a no-till method, meaning it disrupts the soil structure. We understand their point, but our soil texture (i.e., clay), rock problem (i.e., many), and nutrient and pH readings (i.e., hungry for some minerals and acidic) provide an ideal situation for double-digging. Not to mention two ready, willing and able bodies to dig, dig, dig.
I could write a book on double-digging, spelling out the pros and cons. But I won't (and would rather read Seymour's). We will just continue to report on our lessons, techniques and production using this method (which could turn into a quasi-experiment if we get too tired and our latter-dug beds end up being single spade-lengths).