Is it a herbaceous peony(soft green stems) or tree peony(hard woody stems)? If it is a herbaceous peony, you can cut back so that the stems are about 1-2 inches. If it is a tree peony, do NOT cut the stems or tips off. Just trim off the leaves. Take the plant off the pot and wash off the soil as completely as you can. Let the roots dry out for a day. If herbaceous peony, you can trim off the roots so that you have sufficient roots for the number of eyes that you have. Once the root is dry, pack it in moist peat moss in a plastic bag, box it up, and send it. If tree peony roots, it is best not to trim too much off and try to find a box that fits it. For tree peony, you don't have to dry the roots. You can just use damp paper towels or newspapers to wrap the roots portion of the plant, and stick the roots with the wrappings into a plastic bag. Use something to tie the plastic bag to the stem so that it is secure.
Here is a pic of a good herbaceous root:
I can't find a pic of a tree peony root at this time. When I find it, I will post it. If anyone has other ways of doing it, please feel free to share your method.