Fill a seed-starting tray with low-acid sterile compost. Pack the compost firmly into the bottom of the tray. Rough-up the top quarter-inch of the compost by raking your fingertips across the surface.
Mix the mugwort seeds with an equal measure of fine sand to make them easier to sow. Sprinkle pinches of the seed and sand mixture across the surface of the compost in the nursery tray.
Spray the compost heavily with a plant mister to settle the seeds. Moisten the soil to a depth of a quarter inch. Maintain moisture at that level while the mugwort seeds germinate. Do not allow the compost to dry out completely until after the seeds have sprouted.
Move the seed-starting tray near a large, unshaded window. Set it on a propagation mat. Set the temperature on the propagation mat to between 68 and 70 degrees F. Turn off the propagation mat at night.
Watch for germination 10 days after sowing the mugwort seeds. Thin the seedlings so they have at least half an inch of space between them.
Transplant the mugwort seedlings into 4-inch plastic pots filled with loam once they grow to 1 inch in height and have one pair of true leaves, which are silvery-green with lobed edges.
Keep the individually potted mugwort seedlings near a window as they establish a mature root system. Water them once a week to a depth of a half inch. Allow the soil to dry out slightly between waterings.
Transplant the mugwort plants into a permanent pot or bed after all danger of frost has passed and daytime temperatures rise above 65 degrees F. Space the plants at least 18 inches apart if growing them in a bed since they grow very large and require a lot of room to spread.