Dig up the Dogwood
Determine how big the rootball should be on the dogwood. If the tree is less than one inch in diameter, a rootball one foot in diameter and one foot deep will be sufficient. If the tree is between one and two inches, the rootball needs to be two feet in diameter and at least one and a half feet deep. I would not recommend moving a dogwood more than two inches in diameter.
Prepare the new hole for the dogwood. The hole should be at least one foot larger in diameter and one foot deeper than the rootball. Fill the bottom of the new hole with one foot of top soil, available at any garden store or nursery.
Dig up the dogwood you will move. Insert the shovel at an angle toward the center of the tree on the edge of what will be the rootball. Do this around the entire perimeter of the dogwood until it is completely severed from the surrounding soil.
Lay a burlap sack or tarp beside the dogwood.
Gently lift the dogwood and its rootball from the hole, and place it in the center of the sack or tarp. Then wrap the sack or tarp around the entire rootball. This will prevent you from losing any dirt while moving the tree.
Place the tree in the wheelbarrow and move it to the new hole.
Replant the Dogwood
Lift the tree out of the wheelbarrow and place it on the ground beside the new hole.
Unwrap the burlap or tarp from the rootball. Gently place the rootball in the center of the hole. Press down firmly on the rootball to make it level with the top of the surrounding soil.
Fill in the gap between the rootball and the edge of the hole with the remaining top soil. If there is not enough to make the soil level, use some of the dirt that was removed from the hole to top it off. With your foot, firmly press on the soil around the dogwood to hold it in place.
Water the dogwood thoroughly every day for at least one week to reduce shock and allow the roots to become established.
Fill the hole created by removing the dogwood with the leftover dirt from the new hole.