My method is similar to Saphire's, except I don't bother with sewing the bias strip inside out, then turning it right side out. I stitch it right side out (wrong sides together), trim the seam allowance to 1/8", and press it flat with the seam hidden on the bottom. Then I pin or glue baste it to the background.
You can machine stitch it with a straight stitch, buttonhole stitch, or hand-applique it in place.