“Shroud usually refers to an item, such as a cloth, that covers or protects some other object. The term is most often used in reference to burial sheets, mound shroud, grave clothes, winding-cloths, or winding-sheets, such as the famous Shroud of Turin or tachrichim (burial shrouds) that Jews are dressed in for burial, or the white cotton kaffan sheets Muslims are wrapped in for burial .” Wikipedia
There is no mystery here. You can purchase a shroud from eBay, Amazon, or a host of religious and non-religious providers you can find on the internet. If you have a quilt with historical significance to your family, or a stunning sari you bought on vacation, you can personalize your shroud. A simple piece of linen or silk painted by the artists in your circle (amateurs and professionals) can do the job as well. For a Green Burial, you want to use a natural fiber with natural and non-toxic inks.