One pillowcase will form the outside, and the other will be the lining. Lay both pillowcases flat and cut out the pattern below. Measurements below are for a fairly small bag- feel free to add as much length as your pillowcases allow, or adapt the pattern once you've made your first tester bag.You will have two outside pieces (blue) and two lining pieces (taupe).
If you want a pocket, sew one to the good side of a lining piece now.
Lay one outer (blue) piece on top of one lining (taupe) with right sides together. Starting at one upper edge, sew upwards along the curve, over the top of the handle, and down the other curve. (Click photo to enlarge to see the sewing line). Clip the seam (if you're not familiar with this technique, it means make a small snip in the seam every 1/2 inch or so. It allows rounded seams to turn inside out easily and smoothly). Don't sew the two sides or bottom closed yet.
With right sides together, lay the front piece over the back piece. Sew up the two sides and bottom seam. (This is the view from the inside.) I apologize for the wonky seam - I sewed and photographed this up in a big hurry during Little V's nap since the pretty tutorial I photographed last night was too dark. On the plus side, I now have these bags down to 30 minutes each.
Here's how to square the corners of the bag: from the inside, take the bottom corner of bag and pinch sideways. Sew a line across where my finger is pointing.
Last thing: either tie the two handle pieces in a knot for fun, or overlap them on the ends and sew shut like I've done here. You can top the stitching with a button.