Remove all branches up to 1 inch in diameter with loppers. Use a hand or power saw to remove all larger limbs. Remove all debris from around the skeleton of the bush.
Dig a trench around the bush with a spade, cutting through the roots as you go. Remove the soil. Shove the spade up under the root ball all around the bush and try to lift it out of the ground. A spade should be sufficient to remove smaller bushes.
Use a mattock for help removing larger bushes. Use the ax end to chop any large roots and the wedge end to go under the root ball and lift the bush up. Alternate chopping and lifting until you can safely remove the shrub from the hole.
Place large shrubs on a tarp to drag them to the curb or disposal site. Remove any remaining roots from the hole and refill it. Tamp the soil down well several times to make sure the hole is solidly filled and will not collapse.