Plant 2–3' apart with the eyes (where the growth shoots meet the root) no more than 1–1½" below the surface in well-drained soil, full sun to partial shade.
Peonies are extremely long-lived so amend the soil richly when you plant. Compost, very well-rotted manure, bone meal and azomite are all recommended. After that they need only a bit of weeding and feeding to flourish.
Mature plants often need staking or tying because flowers and buds can be quite heavy. For big plants, I’ve been using a chicken-wire method that Mary Fowler recommended. Cut a flat circle of chicken wire 2 or 3' in diameter and place it on the shoots when they are 8–10" tall. The shoots lift the wire, grow through it and use it for an invisible support.
Remove spent flowers after blooming, then cut dead foliage to near ground level in fall.
Plant along the driveway; a heavy snowbank doesn’t bother them.
Herbaceous Perennial Plants
When you receive your order, open the bags and check the stock. Roots and crowns should be firm and pliable. If they are slightly dry, add a little water or, if they are going to be potted up soon, wet the roots. Generally, a little surface mold is harmless and will not affect the plant’s future performance. If you cannot pot them up immediately, store them in a cool (35–40°) location for a short time.
Do not plant bare-root perennial plant crowns directly outdoors.
Pot up the rootstock using well-drained potting mix in a deep 6" pot or a 1-gallon container. Avoid coiling the roots in under-sized containers.
Grow newly potted perennials for a few weeks in a protected location in indirect light at 50–60°. Wet and/or cold conditions for an extended period may cause rotting.
Transplant outside once they show some top growth and the danger of frost has passed.
For more info:
About planting bare-root perennials.