Lay your shirt flat and cut a square out of it, through both layers. Cut as close as you can to the neck ribbing and the armscye seams so you can get the largest square possible from one tee.
Pin the square pieces, right sides together, at the sides and the bottom.
Sew the sides and bottom together. Do not pivot at the bottom corners; instead round them off (this little trick will be a lifesaver if you ever spill any small objects in the bag; this also prevents dust and dirt from collecting in the corners).
If you have an overlocker or serger, overcast the raw edges to prevent unraveling; if not, use a zigzag stitch on your sewing machine.
Measure about 1 3/8" up from the upper line of stitching on the t-shirt's remaining hem piece, and mark. Make another mark at the same place at the other side of the hem piece.
Cut straight across.
Fold the raw edge of the hem piece under itself and sew it down, matching the stitching line of the hem.
This will become the handles for the bag.
Cut the hem piece into two pieces.
Pin each piece to the underside of the top part of your tote.
Fold the end of each piece under just prior to sewing it for added strength.
Sew around the edge of the handles, making a square with an "X" through it. This is an exceptionally strong stitch, used commonly for tote handles, and can withstand a lot of stress.
You're done! Since the bag is made of stretchy knit fabric, it will conform to the shape of what's inside, and can stretch if you load it up too heavy. You can slip a piece of canvas or some other strong woven inside near to bottom to prevent this - otherwise, hang from your shoulder and declare your love for the Big Apple!