Hi Monika, welcome to the peony forum! Dividing and moving peonies isn't really complicated but it is labor intensive if the plant is large. Dividing is the ONLY way to ensure you have more of the same plant since they don't grow true from seed. If you have a peony that's mature--lots of stems and flowers this spring, you can divide it to make multiple new plants. First off you'll want to wait until fall when the plant goes dormant. Peonies will die back to the ground every year, they don't have to be THAT far gone but if you can wait until most of the leaves are dried up it would be best since they're still storing energy for the next year until then. It's easiest to cut back all foliage at that point so there's only a few inches left--less to get in the way. You'll want to dispose of the foliage rather than composting it to get rid of any disease/mildew/etc. Start digging at least a foot out from the outer edges of the base of the stems as some varieties have massive roots. You'll want to dig down at least 18" and lift the entire thing out. Once you've dug all the way around it and down you should be able to rock it gently with the shovel--if you still feel a lot of resistance you'll want to go deeper. Once it feels like the roots are loose you'll have to lift the entire root out. (Most of the time there will be pieces that break off--pretty much unavoidable and not a big deal but save any larger root pieces--some peonies can grow from pieces of root even if they don't have eyes.) Use a water hose and remove as much soil as possible so you can get a good look at the root; it'll be a big jumble of feeder roots with eyes like on a potato on and near the crown of the root. You'll want to examine it before cutting to get an idea of how many divisions you can make, you'll want 3-5 eyes and 1-2 complete feeder roots/division. Sometimes you can pry the whole thing apart but most of the time you'll need to cut from the crown down to get the division started, a fine tooth saw or knife will make it easier but make sure they've been cleaned thoroughly first. I typically go right down through the middle of the root first cut then gently pry subsequent pieces off with little need for a knife. I've seen posts from people in more humid areas than where I live recommend leaving the roots unplanted for several hours to allow the cuts to dry up; I've always just replanted mine right away with no issues. Depending on the variety and the size of your divisions you could easily get flowers on your divided roots next spring.
Growing from seed is pretty cool as well--you could end up with a brand new, amazing peony that no one else in the world has! It does take a lot longer to get to blooming size, I personally think 3-4 years is way optimistic but maybe I'm just in a more challenging growing zone. Unfortunately even seedlings from big double peonies typically have less petals and are smaller unless you're very lucky or are a talented hybridizer. That said, I've seen some really pretty seedlings shown by forum members so it's certainly worth trying.
