Remove all items from the shed.
Screw four 4-by-6-inch wood studs horizontally across center of the walls on the shed's interior if the shed is not sturdy. Use 5-inch long wood screws to attach the wood studs. The studs will reinforce the walls and prevent them from bending or swaying during the move.
Dig up soil that buries the bottom of the shed, and then create a small trench around the shed. Remove all of the soil that surrounds the corners of the shed to expose the corners.
Slide one hydraulic jack under each of the two front corners of the shed, and use the jacks to raise the shed. If the ground is soft, place a piece of wood or a brick under each jack to prevent it from seeping into the soil. You may use two more hydraulic jacks to raise the back of the shed if necessary.
Install two tow hooks to the bottom front of the shed, placing one tow hook on each end.
Secure one tow strap to each tow hook on the shed. Hook the tow straps to the tow hooks on a pickup truck that is at least a 1/2 ton V6. A truck at least that size is necessary to provide enough torque to move a 12-by-20-foot shed.
Start the truck's engine, and slowly drive the truck forward to drag the shed to its new location.