My college roommate learned this technique in an art class, after which we used to "borrow" garbage bags from the maitenance closet and make rain covers for our bikes and portable hampers/laundry baskets.
I saw an article in a book that recommended using newspaper bags, but that produces a small piece after folding, which means ALOT of sewing to piece it together. Plastic bags from the grocery store would work as well.
Plastic garbage bags
Wax or Parchment paper
1. Fold the bag to make at least 8 layers (in half, then again), or if you need it to be extra strong, fold once more to make 16.
2. Cut off any seams, handles, or drawstrings.
3. Cut two pieces of wax paper 4 inches longer than the length of your bag.
4. Pre-heat your iron. On my iron, at my house, with my garbage bags, the highest of the dry settings, Polyester/Rayon, is perfect. You'll need to experiment with your equipment.
5. Sandwich the garbage bag between the two pieces of wax paper, and lay the sandwich on the ironing board.
6. Press down the iron, with medium pressure, and keep it moving. One minute per side should work well. Take extra care to seal the seams and edges. You'll see a change in the waxpaper.
7. Flip the sandwich over, and iron the other side for minute.
8. Peel off the paper, and check the ends. If they're sealed, you're cool. All the layers should be fused together. Make more, then sew them together.
What you do with it is up to you, but I might recommend some reusable grocery bags. It's like double-recycling!