Double digging is done to break up compacted soil, to allow air and moisture to penetrate into the ground, enable plant roots to reach deeper into the soil and to dig in compost, manure or fibrous material.
Starting at one end of the plot, dig a trench to twice the depth of a spade. Put the excavated soil in a wheelbarrow, for later use. Fill the trench with a couple of inches of well rotted manure or compost. Dig a second trench filling the first trench with the excavated soil. Fill this trench with a couple of inches of compost. Continue with this method until the end of the plot. Use the soil in the wheelbarrow to fill the last trench. Don't worry too much if you have big lumps of soil the cold nights will break these up.