When I did my SunBonnet Sue squares, I used fusible and sewed the fusible side facing the right side of the fabric with a slit in the fusible. Then I turned them inside out so there was a finished seam all around the pieces and ironed them on. Then I secured them with the blanket stitch. I haven't finished the quilt but I have finished the squares.
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I know mine are rather simple, but it worked for me. I am sure many of the ladies will have better ideas. Good luck.