Dry cleaning seems to be the best way to keep  silk in good condition and maintain its original beauty, luster, and texture. However, I've seen claims that this will have a bad effect on the silk in the long term. You can also hand wash it in lukewarm water using the mildest soap. Adding a tablespoonful of clear white vinegar to the final rinse is supposed to be a good tip.

     Never boil, bleach, wring, crumple or soak your  silk for a long period!
     After washing it, roll it up in an absorbent towel or other cloth to absorb most of the water -- but not tightly! Immediately remove it from the fabric roll and dry it in the shade, preferably where there's a mild breeze, and be sure it's well supported. If water drips from the silk then it's too wet.
    Iron  silk on the inside of the garment while it is still slightly damp. Some persons recommend using only a cool iron with the intent of pressing out wrinkles and not heating the fabric. If the silk is already dry and you are using a warm iron, apply a damp cloth on the outside of your silk fabric and iron through the cloth.