There's a really good tutorial on You Tube "Sewing to sell quick & cool grocery Bag" by Virginia Lindsay. We're making them out of corduroy for our Homemaker's ladies.
I've also made them out of upholstery fabric.
There is another pattern on You Tube where the bags and the straps are one piece - rather than make straps and attach them to the bag. Sounds like a good idea, too, but it uses more fabric. hmmmm........