Hang your textile art in a place out of direct sunlight. Avoid a place too close to the kitchen, where it may be unnecessarily exposed to smoke, flour and food dust, and grease.
Hang using an acrylic drapery rod, or sealed wood. The ends can be decorated with finials. It is also possible to have the piece stretched professionally over a frame. Or mounted in a shadowbox.
Dust when necessary with a clean feather duster reserved for textiles.
After a number of years, or for a particularly dirty textile clean with a vacuum cleaner using an upholstery brush reserved for textiles. Use a dabbing motion (up and down) instead of side to side. For fragile work, place a clean screen (reserved for textiles) over the textile first and vacuum through the screen. Move the screen and repeat. Turn the textile over and repeat the process on the back. Alternatively, attach the screen to the upholstery brush and then vacuum. Types of screening: cheesecloth, mosquito netting, fibreglass screen, other…)
Refrain from touching your textiles too much, as finger oils are very harmful. In museums the curators wear white cotton gloves when handling antique textiles.
Research on the internet, a great source of articles on caring for art quilts and textiles in general.
When not hanging, store in an acid free box wrapped in acid free tissue paper. Alternatively, if you have a spare bedroom, store large textiles on the bed flat, with acid free tissues between the layers. Keep the edges sealed with clean sheets to keep out moths. Do not wrap in plastic except for short periods during transport.