A double-dug bed is made by digging it all one spade deep. Then you start over by digging a trench, loosening the bottom of the trench down another spade length, then cascading the trenching and digging over the entire bed.
It's a ton of hand work, but allows veggies to be planted at amazingly high densities, with many times the yield per square foot, compared to traditional methods. Tobacco grows wonderfully in a double-dug bed, but it has quite a bit more wind sail effect than, say, bush beans or peppers. In a deeply dug bed, weeds can be gently pulled out, roots and all. (But that's probably why the tobacco blow downs are more likely.) The dense planting also creates its own ground shading, acting like a natural mulch.
Composted manure is initially applied to the surface, then is well distributed into the soil during the extensive digging.
Deep digging cannot be used well with mechanical tilling, since tillers (and your feet) sink to China. So it's limited to beds of about 5' in width (any length). Once double-dug, a bed can't be walked on. You have to work it from the side. Double-dug beds should carry a warning: Ask your doctor if you are healthy enough to engage in double-digging.
Bob
