Most herbaceous peonies are pretty easy to divide. Once they're out of the ground, spray the roots with a pretty hard spray of water to get the remaining dirt off and see what you have. You'll probably see a big twist of roots with little pink or white eyes (like those on a potato that's left for a while) clumped near the base of the stems. If it's a big clump it's easiest to use a shovel or spade to split the root into a couple of pieces. Most of the time you can gently twist/bend the remaining pieces and natural places to cut to divide will be apparent. Make sure you leave a couple of the big, fleshy roots attached to the eyes and that's it. Cut the stems down to an inch or so and replant your newly divided roots so that the eyes are pointed up and around an inch under ground when fully covered.
I've see it posted that it's easier to divide them once they've been out of the ground for a day, the roots are supposed to be less brittle. I've always divided mine as soon as they were dug so I'm not sure which is best.
Peonies are pretty forgiving plants and the roots can withstand quite a bit of manhandling. Some of the feeder roots will probably break off as you're trying to get it out of the ground. If you leave them planted where they broke off some varieties will form new eyes and create a new plant that way, too.
