Love yourself and your silk.
Silk should be washed in cold water (hot water can dramatically change the feel of your silk) by hand with a neutral pH level. You can find this in most baby shampoos or mild/natural soaps. A pH level of 7 is considered neutral. I use Dr. Bronner's Castille baby soap to wash the silk free of dye, and it is a good option for continual cleansing. The better you take care of your silk, the better it will take care of you.
Silk tends to wrinkle relatively easy, but it can also fall quickly. You don't have to iron it, but be sure to hang it up so the wrinkles can fall out. When ironing, be sure to dampen the silk with a spray bottle of water or run it under cold water and pat until damp. If not ironed while damp, you may run the risk of burning. Place a divider (cotton) between the iron and the silk for further protection.
Most dyes, both natural and synthetic, will fade if exposed to sunlight for prolonged periods of time. Keep your silk in a cool, shaded area (like your closet or in a dresser drawer) to avoid this!