Vegetative: The white wood aster tends to grow somewhat colonially, spreading slowly by underground rhizomes. Less commonly, it will spread by layering, with the stems rooting from nodes. You can reproduce this plant both by division or by layering.
For division, isolate a stem or group of stems that is growing from a clump of these flowers, and dig them up, separating them from the root system and transplanting them to a new area. The disruption of the root system may cause some of the leaves to wilt, but my experience is that these plants usually transplant easily, and after a month or so, they will be growing again.
For layering, bend a stem to the ground and cover it in soil or leaf litter, then return later when the buried part of the stem has grown roots, and separate it from the original plant. Again, cutting the source stem may cause the leaves to wilt, but the plant will soon recover.
Shelter new plants that you have transplanted, divided, or layered, making sure they get ample water and are not exposed to too much direct sunlight.
From Seed: This plant is relatively easy to grow from seed; however, you may need a lot of seed in order to get good germination. Because seed production is small though, I recommend being cautious about gathering seed from wild populations. Only gather from the wild in areas where this species is abundant.
If you don't want to bother growing the plants yourself, you can look for seedlings, which are often common around the parent plants. But if you want to grow the plants yourself from seed, gather them in late fall or early winter, once they are mature but before they blow away in the wind. Sow seeds in fall and many will germinate in spring. If conditions are right and you use a lot of seed, you may even get some germination by merely scattering the seed, but keep in mind the seeds are loved by wildlife so many will get eaten if you scatter them.
Watch carefully for the tiny seedlings. In shade, seedlings will grow slowly and may only reach a couple inches in height by the end of the first year.