So, I gave it a go. Be kind, this is my first tutorial. Constructive comments and suggestions welcome.
I didn't "line" the bag in the traditional way; there are still visible seams on the inside. But the bag is much stronger than one t-shirt alone.
Find two t-shirts that you like the graphics from. Preferably, the t-shirts would be the same color fabric, but you could get funky and do two different colors.
1. Cut along the green dotted lines of your first t-shirt. I prefer to use a rotary cutting tool, but scissors would work, too. Cut the waistband off first, then cut through both thicknesses of t-shirt. Make sure you leave a good couple inches between the top of your graphic and the top of your rectangle, or your graphic will be too close to the top. Save the t-shirt sides for the handles, and the waistband for the top banding.
2. Lay one of the rectangles from this shirt over your other shirt. Cut around your top rectangle through both thicknesses of that shirt. This should help make sure your rectangles are all the same size.
3. With t-shirt graphics facing each other in the middle of the pile, layer all rectangles on top of each other. Whatever you want on the inside of the bag should be on the two out-sides. So order is lining-graphic-graphic-lining. Pin together. If necessary, trim to make even.
4. Sew around three sides (along orange lines) leaving top of bag unsewn.
5. I had a hard time illustrating this step. Leaving the bag inside out, open the bag and flatten the bottom a little until it looks like the middle graphic. Sew across the corners of the bottom at a right angle to the side seams (graphic on right). This step isn't necessary. Skip this step if you don't want a flat-bottomed bag.
6. Take waist band of one of the shirts, and cut so it is double the length of the top of the bag. (Make it so it will go around the entire top of the bag on both sides.) Sew ends together. With bag still inside out, and wrong side of waist band facing you, pin the cut side of waistband to line up with top of bag, and so the joining seam meets the edge seam of your bag. Sew along the top.
7. Turn the bag right-side out. Fold waistband over, and iron. Pin (if needed) and sew along the edge of the band. (You wouldn't have to use a waistband here. I like it because it is strong and has one finished edge. You could take a strip of fabric double the width you wanted, sew the raw edges together, turn it inside out, fold over the edges of the bag, and sew.)
8. Take the leftover sides of one or both shirts. Cut two strips of fabric double the width you want your straps, and double the length. Fold each strip in half the long ways (so now it should be as wide as you want your straps) iron and pin. Sew along the unfinished edge. Turn inside out. You should have a tube of fabric. Iron this tube flat.
9. Pin the ends of one strap to one side of the inside of the bag and reaching the edge of your band. Using the same color thread as your band or a complementing contrast color. (This stitching will show) Sew along the edges of the strap and band in a square, and then in an "X" through the square, as shown in the last drawing. This makes your stitching good and strong. Repeat on the other strap.
Congratulations! You have a tote bag!