How to wash silk

Silk is a natural and delicate fabric. It's chemically quite similar to human skin. It’s soft, supple and smooth and it absorbs perspiration while letting your skin breathe
Fill a bucket with cold to luck-warm water and 60ml of white vinegar (or a drop of  baby shampoo, or silk or wool detergent) –You may gently rub some Marseille soap on stains, if it's the case.
Rinse with cold running water. 

You may want to soften the shirt by soaking it in water and white vinegar (1/2 glass per 2 litres/67.6Oz of cold water) for 10 minutes and rinse it with cold running water.
Lay the wet shirt flat onto a white absorbent towel and roll it up to get rid of excess moisture. Then lay it flat on a drying rack or on a dry towel. 
Dry in the shade. 

Don't use bleach
Don't leave silk under direct sun light
Don't use water when ironing
Don't spray deodorants or fragrances
Don't wring silk
Don't use hot water
Don't dry-clean (yes, you can take it to a professional, but they'll need to wash it by hand)

Low heat. Use a cloth between iron and silk. Turn the item inside out and iron on the reverse side of the fabric on a cotton-covered ironing board. Use a low setting and don't use steam, which can leave watermarks. 

Camixa LETE Green Sand-washed Silk shirt for women
Sand washed silk looks like peach skin: it's slightly velvety. When ironing, you might see some darker shades that, at first sight look like marks (this happens rarely, especially on darker colors). To bring the look "unified" (no shade spots), rub the silk with your finger in the opposite direction -think of velvet. It will be instantly back to perfect.
Colored: fill a bucket with lukewarm water, wool or silk washing-liquid, 1 spoon of salt. You can opt for Marseille soap (leave some in the water) and rub it gently on the fabric. Leave the silk in water for 15 mins. and rinse it with cold running water. Now soak it in white vinegar (1 glass per 2 liters of water) –this step is for softening the fabric. Rinse again and hang it! 
White: Do as above. Before the vinegar- softening treatment, add 2 spoons of Hydrogen Peroxide (30-40V) in the water. Close with a lid. Rinse with vinegar as above. If it has yellowed, it smells or visibly dirty, soak it in warm water (not hot), add 3 spoons of salt, the juice of 2 lemons (one lemon juice for each litre of water). Close it with a lid and leave it for several hours/one night.
Always follow the labels instructions.
What & Why
Vinegar softens, neutralizes smells, revives colors
Salt preserves colors and helps dissolving dirt spots
Hydrogen Peroxide is a delicate whitener