Start by digging up the plant. Push a sharp-blade spade into the soil a few inches away from the clump of stems, with the blade angled underneath. Work from all sides, and as you go, push down on the handle of the spade to lever the root ball up. Once the shrub has been dug up, separate the clump into pieces consisting of a shoot and roots. Do this by spreading the branches so you can look down into the clump, then chopping down into it with your shovel, or, if necessary, an ax.
Some shrubs have horizontal, underground stems that can be cut free with just a lopper.
If the shrub is very old, save only root and shoot pieces from the outer edge of the clump. These are the youngest and most vigorous, so they make the best new plants. If your shrub is not too old and you just want a few new plants, dig up a few shoots from the outside of the clump without disturbing the plant. Inspect pieces for replanting and re-cut any torn roots or underground shoots cleanly with a pruning shears. Shorten stems if they are so long that the new plant will be unsteady in the ground.