Buy healthy, green plants with no signs of wilting or disease. Plants should be stocky, with plenty of leaves. It's actually a plus if they don't have any flowers on them - they'll divert their early energy into root development rather than flowering.
Choose a site in full sun to light shade. Sweet alyssum likes average to poor, well-drained soil and moderate water.
Plant seedlings in early spring, about two weeks before your region's last average frost date. Position 6 to 8 inches apart.
Keep soil a little on the dry side.
Trim faded flowers to promote longer blooming. If plants look ragged in mid summer, shear back by half to rejuvenate them.
Tear out and discard plants in fall, after frost fells them.