The most common form of propagation is crown division in the fall when the peonies are dormant, so late summer is prime time for peony planting/dividing/transplanting. September and October is when most root growth occurs.
Cut off the leaves and stems close to the ground. Carefully lift the clump, taking care not to damage the roots, and wash off the soil with a garden hose. Use a sterilized, sharp knife to cut the crown apart. Each division should have two to five eyes. If the divisions are to be planted in the same garden it is not necessary to trim up the roots.
Planting depth is important. On clay soils, the eyes should be 1 to 2 inches below the soil surface. On lighter soils, sand, sandy loam, etc., the eyes should be 2 to 3 inches beneath the surface.