Hand wash or machine wash cold, gentle cycle and hung to dry. Use a mild, environmentally friendly detergent.
When machine washing, turn garments inside out - this reduces friction on the surface of the garment while wet, which helps prevent fading.
Linen enjoys a nice water spritz from a spray bottle when ironing on a steam setting, this will soften the linen after wash.
The silk is a-ok to iron too, just use a lower heat setting.