Dividing & Transplanting: The easiest way to propagate asters is to take a division in spring. This will serve a double purpose of creating new plants to share with friends and reducing the size of an overgrown plant. Asters should be divided every 3 to 4 years so they don't get too large. Spring is also the best time to move an existing aster to a new location. In spring, after the ground thaws and plants start to grow, dig up the aster plant and make 6 to 8-inch diameter divisions with a group of leaves and roots. If you want to create just a few divisions, you can separate out pieces from the mother plant along the edge of the root ball, leaving the main plant intact. Replant the division immediately and keep well-watered.
You can also take cuttings of your favorite aster to propagate. In late spring take 2 to 4-inch long cuttings from the stems of the plant. Remove the bottom leaves, dip the cut end in a rooting hormone powder, and stick the cutting in plastic pots filled with loose potting soil. Place the cuttings in bright area out of direct sun and cover the cuttings and pots with a perforated clear plastic bag. Keep watered when dry and they should root within a few months.
You can also collect and save seeds, but it will take a number of years to grow a sizeable, flowering plant.
Cut back aster plants in fall after the foliage yellows to about 2 inches off the ground. Compost the tops.