Plant peonies in full sun or part-shade in a good garden soil that is neither too dry nor too wet.
Enrich the soil with plenty of organic matter before planting.
Ensure the roots/plants are planted so that the pink/red buds are at soil level (you should just be able to see the highest buds). For potted plants this probably means the same depth as they are in the pot. If you plant peonies too deep it will inhibit flowering. Also, don’t mulch over the plants as this is the same as planting deep.
Although the soil must not be too wet it is important that the plants do not dry out when the flower buds are forming, therefore if April & May are very dry watering may be required.
If you have peonies that are planted too deep, wait until end of September and then lift them. Re-plant them as above ensuring that the new buds are at soil-level, so that when they swell, they will be fully above the surface. It is the frost and cold on these buds that triggers the plant to create flowerbuds.
It is also a good idea to give the plants a good feed (of a general garden fertiliser) after flowering has finished. This will give the plant a boost for the next season and bud production.