Wet viscose is fragile — that's the whole game. Viscose, rayon and modal are regenerated-cellulose fibres that lose around half their strength the moment they get wet, so a damp garment tears and pulls out of shape far more easily than it looks. Every rule below comes back to handling it gently while it's wet.
Wash cool, and check the label first. Many viscose pieces are labelled dry-clean-only — follow that, and never wash a garment tagged as such. When it is washable, hand wash in cool water up to 30°C with a mild detergent, or machine wash inside out in a mesh bag on a delicate, low-spin cycle. Don't soak it longer than about half an hour.
Never wring, and reshape while damp. Press the water out — don't twist or wring, which snaps the weakened wet fibres and pulls the garment out of shape for good. Lay it flat or drip dry, easing it back to its proper shape while it's still damp. Keep it out of the tumble dryer, which shrinks it.
Iron cool, on the reverse. If it needs pressing, use a cool, low iron on the inside while the fabric is slightly damp, keep the iron moving, or freshen it with a steamer instead.