furoshiki bag

The furoshiki is the original "eco bag". These squares of fabric are most commonly thought of as being used to wrap gifts, but they are also used in décor and  to carry things. This video does a good job of explaining the basics of using your furoshiki as a bag, including a very important tip on how to tie and untie corners:

Of course you don't have to use a furoshiki, any square of fabric will do, including scarves and bandannas.