Normally Asters are propagated from division. Dig up a piece of the plant and pot it up. Annual ones are grown from seeds.

Very young emergent shoots in spring might root but as Ob says, division is the norm.

There is one Aster which is propped from cuttings. A ericoides var prostratus (I think). This has very woody stems and does not seem to produce lots of new shoots from below ground like the other types do.