The months of April and May are excellent. In the fall, late August through September is optimal. Cut a circle around the crown of the plant with a trowel or spade, then pry the roots up and out. For large perennials it is easier to cut the plants into manageable pieces when they are still in the ground. Don't remove shrubs unless their presence isn't part of the new plan.
Some perennials prefer a certain season for division or transplanting.
If you are renovating at the wrong time for these plants, it is better to work around them. After digging set the plants on a plastic tarp spread out in a shady, protected location. Water the plants as weather conditions warrant to prevent them from drying out. Under good conditions, most plants will survive out of the ground for a few days without any problems. After the plants have been removed from the bed, carefully remove all weeds, and rake the soil level.