Nylon and rayon fabrics typically have an instruction label that tells you to dry-clean the fabrics only. However, it is possible to clean those fabrics at home without damaging the item.
Wash nylon fabrics in a washing machine with warm or cool water. Rayon fabrics are less strong and require hand-washing, which won't damage or weaken the fabric. Dry rayon fabric flat on a white towel, and place nylon fabric in a dryer on its lowest setting.
When washing nylon fabrics, pour fabric softener into the washer during the final rinse cycle. This removes any static electricity.
If you need to wash rayon fabrics quickly, place them in a net bag and wash in cold water without any other clothing. Rayon is very weak when wet, and may get torn or otherwise damaged if mixed with other clothes.