Amy,
I love my peonies too, but so far, I haven't had to split them. Soooo, I don't speak from experience, but in my favorite perennial book, it says to "lift plants in late summer, wash off the soil, and cut the roots into sections with 4-5 eyes each. Use a sharp knife and make clean cuts. Replant divisions into enriched soil."
It also says plants may grow undisturbed for years and to split when they get overcrowded or if soil gets "impoverished". If you decide to split and find the root ball isn't that large, you might only split it into two pieces instead of 4-5 sections.
Hope this helps. 