When you are dividing perennials, try to do it at least six weeks before the predicted time for a hard freeze in your area. This gives the plants time to settle in and get their roots established in their new site before they are stressed by extremes of temperature.
Remember that both peonies and iris like to be planted in shallow holes about 1 to 1.5 inches deep. Most other perennials benefit from a wide deep hole with loose soil for their roots to maneuver.
Always tamp down the earth around each plant once it is installed to get rid of any air pockets below soil level. Then water well daily for two weeks as this also gets rid of air pockets and settles the plant into its new home, as well as provides it with essential hydration as it adjusts to the shock of relocation.
Survey your garden and try to imagine it in spring and summer and identify dead spots and relocate new divisions to those. Think about what will be blooming at the time of the perennial that you are relocating. For example, last year I divided some small purple iris, which did not need a deep hole so were easy to move about. In the spring, I was pleased to see that the repetition of splashes of purple throughout my garden really integrated my other spring bloomers.