Fiber or mixed-media artwork is, in general, no different than caring for a painting or other artwork:
Hang all artwork away from exposure to direct or reflecting sunlight and strong, constant (especially fluorescent) lighting.
Avoid exposing artwork to high temperatures, high humidity, or smoke.
If you need to store a fiber artwork, roll it front-side out (to avoid wrinkles) in 100% cotton fabric that has been washed, in acid-free tissue paper, and/or in an acid-free box. Do not place your textile artwork directly against wood for long-term storage as the oils in the wood or wood finish can transfer to the textile artwork.