Sow alyssum seeds from late March to May at 15-29C (60-85F), on the surface of a good quality seed compost and gently firm down. Keep the soil damp but not wet and do not exclude light. Place in a propagator or seal the seed tray inside a polythene bag until after germination, which usually takes 7-30 days. When seedlings are large enough to handle, transplant and grow them on in cooler conditions until large enough to plant outdoors. When alyssum plants are well grown and all risk of frost has passed, acclimatise them to outdoor conditions over 7 to 10 days. Transplant outdoors in full sun on light sandy, well drained soil at a distance of 30cm (12") apart. Alternatively, sow alyssum seed outdoors in May, directly into well prepared seed beds.
Water regularly until plants become fully established. Cut back after the first flush of bloom to encourage more alyssum flowers to be produced.