People treat silk as though it will dissolve. It will not. It is a protein fibre, closer to hair than to cotton, and it wants the same things hair wants: cool water, neutral pH, and not being twisted.
Cool water, neutral soap
Cold or lukewarm, never hot. Ordinary laundry detergent is alkaline and enzymatic, and enzymes designed to break down protein stains will happily work on a protein fibre. Use a pH-neutral wash or a plain unscented soap.
Do not wring
Wringing breaks the fibre where it folds and you get permanent puckering along the crease. Press the water out against the side of the basin, then roll the piece in a dry towel and press again.
Dry flat, out of the sun
Hanging wet silk stretches it out of shape at the shoulder. Sunlight fades it and, on sand-washed silk, dulls the surface within a few wears. Flat, shaded, moving air.
Ironing
Lowest setting, on the reverse, while the piece is still slightly damp. A hot iron on dry silk scorches it in a way that does not come out.
What about the washing machine
A cold delicate cycle in a mesh bag will not destroy a heavier silk, and plenty of people do it. It will shorten its life. For a 22-momme slip that you own one of, ten minutes in a basin is a reasonable trade.