I always think of peonies as a grandmother's flower. It's charming, beautiful, smells wonderful and it lasts for many, many years in the garden with a little extra care...just like a grandmother.
Herbaceous or Garden Peonies (Paeonia officinalis) are great for cold climates, since they withstand freezing temperatures, even in Zone 2. Mulch to be sure, but usually a good snow cover protects the plants. Peonies grow from tubers, and if there are less than 3 "eyes" or reddish looking buds on the tubers they will take years to bloom. Ideally you want 3 eyes per division, and no more than 5. The plants should be planted in a large hole, that has been predug and amended with compost, rotted manure or peat. Plant so none of the eyes are more than 2 inches under the soil. If you go much deeper it will take the plant longer to bloom, as long as 2-3 years. Peonies do not do well with wet feet, so plant them in soil that is very well drained and in full sun. In the south plant them in partial shade to help them survive the hottest days, but make sure they do get enough morning sun and are still well drained. Some very hot areas will not do well with peonies regardless of care.

After your peonies bloom you should leave the foliage, this is how the tubers will feed during the summer. In the fall when they brown you can cut them back to the ground, not before, or it can affect the blooms. In warmer climates it's important that you cut back foliage early enough to give plants 3 months of dormancy, which they will naturally receive in colder climates.

In the spring remove any old mulch, and before the hot weather appears, mulch each plant again with 2-4 inches of organic material. Remove this layer of mulch before winter, and replace it with a mulch of straw or hay. This is a precaution against any bacteria/disease that may be lurking in the mulch. Do not let it touch the stems. You also don't want the buds closer than a couple of inches to the top of the mulch.

Peonies hardly ever need dividing if planted properly. If you notice a decline in the blooms it could mean they are crowded and it's time to divide the roots. This could be 5 years or 50, depending on if they are given enough room to grow. It's best to do this in early fall. Leave them alone if at all possible. (see the note below for other reasons to move peonies.)

I've seen much advice that you should plant peonies in groups of at least three. I don't necessarily agree with this. It depends upon the space you have available. One peony in the middle of a bed with a mixture of tall spring bulbs and summer blooming perennials behind it, and shorter perennials or annuals in front of it can make a pretty flower bed. Peonies are lovely old fashioned perennials and even if you can only have one it's worth the extra love and care for those blooms each year.

PEONY TROUBLES? If your peonies have lush foliage but no blooms there could be several reasons why, according to Organic Gardening magazine.

A very late spring frost may kill flower buds. This is a real concern this year with the odd weather. Cover your peonies if you could get frost. After your peonies bloom and the foliage starts to brown DO NOT cut it to the ground. It needs to be completely dead with no green at all before it's cut back. Your peonies could also be planted too deeply--they should only be planted 1-2 inches below the soil and if the divisions only had 1-3 "eyes" they will take sometimes 2-3 years before they bloom. Peonies also need a good amount of sun, and a well-drained soil. Lastly, if they are planted too near the roots of a large tree or shrub this could be interfering, and you'll need to dig up the peonies and move them to a better location.