Cut back the privet hedge's foliage to within a few inches of the ground with your lopping shears.
Water the ground with a few inches of water. Moist soil is much easier to dig than dry soil.
Dig a trench around the privet hedge's roots to expose the edge of the root ball, using a spade. If you encounter so many thick roots that it is tough to dig, you're digging too close. Widen your circle. Dig until you reach the depth of the root ball.
Wedge your spade into the trench to undercut some of the roots underneath the root ball you just excavated. Push in as deep as you can. Use your foot on the top of the spade to give added pressure. Move around the entire circumference of the root ball.
Lift the root ball out of the hole. Use the blade of your spade as a lever. Wedge it underneath the root ball, then push the handle down to lift the root ball. Repeat on all sides until the root ball is pushed out of the hole.
Refill the hole with a few bags of commercial garden soil.