Rayon (Viscose) is a chemically-altered, natural material. It is formulated from cellulose (wood pulp, bamboo or hemp), treated, and then formed into long, silk-like threads. It's been around since the early 1900's as a fabric replacement for silk. It was especially popular in the 30 & 40's for Hawaiian shirts due to its superior dye absorption, drape, & heat loss qualities. It "breathes" better than silk so was a popular fabric in the humid Pacific Islands.
Keeping it looking its best is a challenge. It doesn't do well in washers--it loves to shred at stitched seams and buttonholes. It loves to wrinkle. And, it is a challenge to iron. Several manufacturers recommend dry cleaning. You can carefully wash it by hand or by machine if using a delicate cycle (not available in our laundromat) with a mild, pure soap. Detergent soaps (those containing phosphates) will leach the colors.
Do not wring it dry. Use towels and roll it like you would a sweater and squeeze out the excess moisture. When almost dry, hang it up to allow the air to circulate and the rest of the wrinkles to fall out. It it is a rayon sweater, use a sweater screen to lay it flat.
Iron using low-heat or you will unbind the chemicals that connect the cellulose molecules.
Start by steaming the fabric without touching it to release the wrinkles. Then, place aluminum foil on top of the fabric while pressing. This will reduce damage to the sheen of the fabric.