With their huge, romantic blooms peonies are a desirable plant and, given that they live for up to 50 years, are really a long term investment for your garden. A common misconception is that they're difficult to grow - they're not!
The herbaceous type (as opposed to tree peonies) are the most common and easy. Fully hardy, all they need is a good position and some support to keep them from flopping. You can either buy or build a cage for support when the plant starts to shoot in Spring. The flowering stems will grow through it and the heavy flowers will do their glorious thing in May or June, even in windy weather.
Peonies like sun and deep, fertile well-drained soil. Before planting make sure you've chosen the best spot, dig deep, and add plenty of soil improver or home-made compost. Don't plant them too deep, they won't thank you! Whilst you can cut a flower or two in the first couple of years, it is better to wait until the plant is well established.
Once they’re settled in (1-2 years), cut them back in Autumn (you may want to wait until mid November, to enjoy autumn leaf colour). Burning the old foliage gets rid of fungal spores, reducing the likelihood of botrytis which can cause peony wilt (mouldy buds and wilting stems) the following Spring. Peonies are not the easiest plant to move, but it can be done in Autumn when dormant. They can be divided too - but dig deep to get maximum root out and try not to disturb the roots too much.
In February/March a light mulch of wood ash, compost or well rotted manure is beneficial, unless they are in very fertile soil. They do not need much feeding (avoid high-nitrogen feeds) and only require watering whilst establishing, and if there is a long dry spell whilst the buds and flowers are forming.
Container-grown peonies are available March-May at the Plant Centre. White-flowering varieties look stunning against a background of evergreens; spring bulbs are a good choice to plant around the base of your clump, and there are many other wonderful combinations - just ensure you allow for air circulation to the stems.