Lay placemats one on top of the other, with the insides facing out and thread a large needle with embroidery floss.
Starting along the bottom seam, begin stitching the two placemats together using either a blanket or backstitch. I did a blanket stitch, FYI. See Apartment Therapy for instructions on various stitching techniques (including a blanket stitch). Note: Be careful that the placemats stay aligned. Your seam should be around 1 inch in from the edge of the placemat.
Continue along the sides of the placemats, but stop your stitch about 8 inches from the top of the bag. This is where you will attach the loops for your strap.
Once you have the three sides sewn together, gently turn your bag rightside out.
For the strap, cut 2 3-inch strips of fabric (I used some trimmings from the interior of the bag, but you can also use small leather pieces, or other fabric you have lying around). The width of the fabric strip doesn't need to be super thick, just durable, since it'll essentially be responsible for holding the strap on.
Form a loop with the first strip of fabric and tuck it between the open seams of the placemats. Make sure it sits right above where your seam ended (about 8 inches from the top of your bag). This way you can fold the top portion of your bag over and the strap will sit correctly.
Pull the loop so that it barely shows on the exterior of the bag. Carefully stitch over the fabric loop (I doubled up on my backstitching to ensure its strength), and continue your blanket or backstitch up to the top of the bag. This can be tricky, as you will have to stitch from the inside of the bag so the stitching matches what you already did.*
Once the loops are securely attached, and the bag is stitched up, string your purse strap through the loops and button or buckle.
Push out the corners in the bottom of the bag to help it lay flat, fold over, and you're ready to go! *If your purse strap does not have a button, like mine, you may have to attach the purse to the fabric loops prior to stitching them into the purse. Just make sure you plan that out before you attach the loops.
**Note: Different types of fabric may require a different technique. You could easily use a sewing machine for thinner placemats, add a liner, a clasp, you name it!