Double digging involves removing the top foot or so of soil, loosening the lower layer of soil and adding amendments such as organic matter, dolomite lime, bonemeal or other slow-acting fertilizers. The added aeration allows roots to move more deeply into the soil, improving drought-resistance and general health of the plant. In very clayey soils or those with so many rocks that digging is difficult, building up the soil by adding organic matter and extra soil on top to make raised beds may be easier, however.
Have a professional soil test done before you begin. The results will tell you the present pH and exactly which elements need to be supplemented, with recommendations on the amounts needed. Have all your amendments handy before you start digging and be sure to have as much organic matter as possible available to add to the soil. Any crop will benefit from extra organic matter in the soil.
Start at one end of your bed and remove a rectangle of soil, making a trench a foot wide, a foot deep and as long as your bed is wide. Use a wheelbarrow to move this soil to the other end of the bed. It will be used to fill in the final trench at that end.
Using a garden fork, loosen the subsoil to a depth of a foot, mixing in whatever amendments you need as you do so. Then dig out another foot-wide trench next to this one, turning the topsoil onto your first trench and mixing in amendments as you go. Repeat the subsoil loosening and amending. Dig another trench, with the topsoil going onto the previous one. Continue in this manner down the bed.
When you dig the topsoil out of your final trench and place it on the previous one, you'll be left with the subsoil at the end. Loosen and amend this, then place the topsoil from the first trench on top, adding amendments as you do.
Rake the bed into a smooth surface, add a mulch if you wish and water thoroughly. The loose soil will make a mound that will settle a bit in the next few weeks. Avoid planting for at least a few days.