Common Name Peony 
Genus  Paeonia 
Species Paeonia Officinalis 
Family Paeoniaceae
Life Cycle  Herbaceous Perennial 
Bundle Size  Bare root bundle of 10 (Spring), whole crate (Fall)
Care

Spring shipping: These plants will ship to you from Vermont in early April. They will just be coming out of dormancy. You may see swollen 'eyes' on the roots, but in general they are in a dormant state and might look a little dead. Don't worry! They will wake up. 

If you can't plant immediately upon arrival, store them in  a cooler to keep them in a dormant state. Plant as soon  as possible into a prepared bed - if you need some time  they can be potted up into 1 gallon pots but this step is  unnecessary. 

They are waking up and will quickly decline if not given  soil, water and sunshine. This is a carefully  orchestrated process to get plants quickly from their storage conditions to you so please do your part and be ready to plant them on arrival. 

Fall shipping: Full crates of peony roots will be shipped out from (Virginia?) in October. They will arrive in a dormant state, ready for immediate planting. If you cannot plant right away, store in a cooler until you are able. Only delay the process as long as absolutely necessary - the root health will decline the longer it is out of the soil. As long as the ground is workable (aka not frozen) it is safe to plant out the roots.  

Netting / Staking Not necessary when grown as a cut flower as flower heads will be cut before they are blown open. If grown in a garden, support is necessary as fully open flowers catch rain and can get quite heavy, often ending up laying on the ground or with bent stems.  
Hardiness Zones 3-8: Peonies need a cold winter and may struggle in warmer zones. 
Spacing 24 - 36 inches 
Soil Preference Loose, fertile, well-draining soil. Neutral to slightly alkaline pH. Peonies benefit from soil that has been lightly amended with compost and granular fertilizer. 
Light Full sun 
Pinching Do not pinch
When to Plant Peonies grow best if planted in the fall, but will still grow  well if planted in early spring while they are dormant and the temperatures remain cool as they establish new roots. 
Days to Bloom 120+ days post planting - do not harvest flowers for  approximately three years after planting. 
Harvesting Harvest buds when in "marshmallow" stage - the point at which they are showing color and are soft when gently squeezed yet have not opened up - for the longest storage life. For the largest possible flower, try disbudding your peonies. This process involves removing any side buds on a stem when they are still very small (the size of a pea) and can be twisted off. This allows the plant to focus all of its energy into the main bud. 
Post Harvest Care If harvested at marshmallow stage, they can be dry  stored in a cooler (at 35F) for two to three weeks.  Remove the foliage, wrap in paper or plastic and store horizontally. Be sure that there is no moisture trapped in the plastic or it may cause the development of botrytis during the storage period. Approximately 12 hours before they are needed, re-cut the ends and place in a bucket with deep water to allow the stems to rehydrate fully. If they are to be used shortly after harvest, place stems in cool water and store upright in a cooler for up to a week. 
Diseases / Insects Botrytis and bacterial leaf spot are both fairly common  diseases found in peonies. They are characterized by  brown or black spots on the leaves, blackened stems  and dead shriveled buds. These diseases are usually  prevalent during prolonged cool wet conditions and  where there is a lack of air movement. Prevent the spread of these diseases by increasing airflow around the plants, avoiding getting the foliage wet during irrigation, and removing any infected matter during the growing season but especially in the fall to try and reduce spore load. 
Bailey's Notes

Although peonies will survive in hardiness zones 3-8 they prefer and perform better in colder zones. They may struggle in zone 8 from the lack an extended cold winter. 

When planting the bare roots, position them with the eyes facing upwards, and cover with no more than 1" of soil. Planting too deeply will encourage foliage to grow with few flowers. 

For the first 3 years after planting, it is suggested that you do not harvest the flowers. Taking the flowers themselves is not the real issue, more so that you would also be taking some foliage along with them, and every leaf is important to the plant at this stage as they are photosynthesizing and helping the roots store nutrients for next years growth. It is for this reason that we suggest when harvesting flowers, only cut the stems as long as you need them and leave as much foliage on the plant as possible.  

Post flowering, remove spent blooms so that the plant  doesn't expend valuable energy on unnecessary seed  production. At the end of the season, around the time of  the first frost, cut the plants back to the ground and  dispose of the dead material to prevent any fungal or  bacterial issues the following spring. 

Resources

The American Peony Society 

Peony Diseases