From Ground: First, water the common peony plant to dampen the soil. This will make it easier to remove the plant without damaging its roots. Next, using a spade or shovel, dig a wide trench around the plant, ensuring to keep the root ball intact. Gently work the spade under the root ball and carefully lift the plant from the ground, trying to keep as much of the root system and surrounding soil intact. If the plant is large, enlist the help of a garden cart or wheelbarrow to transport it.
From Pot: If the common peony plant is in a pot, water it well before starting. Next, tilt the pot and gently pull on the base of the plant. If the plant doesn't slide out, tap the sides of the pot to loosen the soil. Be careful not to pull too hard, as it can cause damage to the plant's roots.