At this time of the year, while there is still some warmth in the soil, most border perennials (although not ornamental grasses an d red hot pokers) can be dug up and shifted around to new positions. Move plants that have grown too large, that have become shy of flowering, that require different conditions from their present ones - or that just look awful with their neighbours. After digging up, most plants will benefit from being divided into smaller sections. The books recommend levering the clumps apart with a pair of garden forks held back-to-back, but who has two garden forks? Instead, rip them apart with your hands and whatever implements seem appropriate while trying to keep the roots undamaged.
Remove any woody, rotten or suspect-looking bits. Replant the divisions in weed-free soil that has been rejuvenated with garden compost and a little sterilised bone meal (wear gloves and don't inhale it) to encourage the roots to grow. Gently water in. If your soil is particularly dry, you may need to water periodically for the next couple of weeks.