Get started by loosening the roots with a garden fork. Gently work the plants out of the ground and shake off excess soil. Perennials form different types of root. Heuchera and Hosta for example are fibrous and pull apart with a little gentle tension.
Hemerocallis form large, tough roots. Use two garden forks and drive them in to the centre of the clump and then levering them apart. They can require some fairly robust pressure so keep trying!
Finally, some perennials create woody, interconnected crowns and these need to be slice apart. Use a clean, sharp spade to make a neat cut through Hellebores or fleshy Delphinium.