This was a really easy idea that I found recently. To make a shopping bag from a t-shirt:
1. Cut around the sleeves (it would probably be best to keep the seam as part of the bag to make it stronger)
2. Cut around the neck leaving at least 4" across the shoulder for the handles (draw around a plate or bowl)
3. Sew the bottom
Note: I lined the one I made using cotton material I had but it makes it a much more difficult task.