Upcycled materials and making your own yarn
Recently I purchased a hat on Etsy. Like every other handmade item I've bought on the site, it was a marvel of craftsmanship. It's also made out of upcycled materials: soda bottles were spun into the soft fiber crocheted into a beanie. It was my first experience with wearing plastic, so to speak, if you don't count all the synthetic fibers surrounding us in modern life.
Apparently, anyone can make "plarn" (plastic yarn) out of plastic bags and then use it to crochet, weave, or otherwise construct new bags, hats, or other designs. RubyReusable has a bunch of links for making plarn, as well as instructions for turning newspaper, VHS tape, dog hair, and old sweaters into yarn.
If crocheting makes you feel all thumbs, weaving may still be in your skill set. See these instructions for weaving with plarn.
The video below shows instructions for making your own plarn.