I break bits off and stick them in pots of gritty compost almost any time chick. They're one of the easiest plants to take from. My older daughter could do them when she was about 6 or 7 adn was thrilled that they grew so easily. I often just break bits off and put them straight in the ground- which reminds me- I did that earlier this year so I'll need to get them moved as they're in the bed that's getting cleared!
I agree, sedum are so easy to grow, and have had almost 100% success with any cutings I have taken.
I took some in September, when i posted this, and they all took - very exciting
They'll even grow from leaf cuttings supposedly with a bit of a heal. Just peal off a leaf and stick it in to some gritty compost. To be honest I've not tried this on purpose, however I have several little plants where a knocked-off-leaf rooted and grew.
We divided a couple of plants a week or two back, and some of the flower stems broke off, so we brought them in doors and put them in a vase. Within a few days they had developed roots.
A few years ago, we split up a clump, and one bit got left lying on the border unintentionally. The following spring it had rooted itself. This is the clump same clump that we've just divided.
From my view they just want to grow whatever you do to them!