Embroidered apparel can be machine-washed cold, inside-out on a gentle cycle with a mild detergent and like colors. You can use a small amount of chlorine bleach, but non-chlorine is the safer option.
If you notice any color residue in water, rinse the garment in lukewarm water and then in cold several times, but try not to rub any stained embroidery. Embroidered clothing can also be dry-cleaned.
After washing, don't leave the clothing to soak or lie in a pile while wet. Don't wring out the embroidered items, but if you want to tumble-dry them, use a cool air setting.
If the garment needs ironing, do it inside-out, preferably between two pieces of cloth. You shouldn't wet embroidery before ironing or use a steam iron.