When it comes to propagating Sedums, it depends on the type that you have. Ground-covering sedums, such as Sedum acre, Sedum album and Sedum floriferum, can easily be propagated using shoots. You can do this by taking cuttings from the shoots and shoot tips and scattering the cuttings on finely crumbled, loose bed soil. Refine loamy soil by adding an extra third of sand. Lightly rake over the shoots and water them with a watering can to increase the contact between the cutting and the soil, which improves rooting.
However, tall Sedums like Sedum telephium are easiest to propagate through dividing. I imagine you are unlikely to have this variety so here is the method for the other varieties:
When the plant begins to shoot, watch for the moment when the young shoots begin to extend between the individual leaves. The shoot also becomes noticeably firmer at this point, and it measure around the same as the width of your hand. You will then need to take terminal cuttings of approx. 10 cm in length and remove enough of the lower leaves that you can plant the shoots in a moist peat-sand mix (1:1, three cuttings in a 10–12 cm pot). Keep the cuttings warm at a temperature of 20–25 degrees celsius. When the young plants become root bound, move them to the bed.
You will often find that even "finished" summer shoots will take root if you defoliate the lower third and then place them in a vase of water. Finally you can also take leaf cuttings from tall Sedums. Pluck the round leaves from the plant in summer to early autumn, cut the end and then insert them approximately one third of their length into a wet peat-sand mix (1:1). Ideally, the cuttings need to be spaced two finger widths apart in a low cutting tray. Pot the plants once roots, buds or shoots have formed, and transfer to the bed when the plant becomes root bound.