The easiest method, IMO, is to apply wonder under or other fusible web to the back of the applique fabric, cut out the desired shape, fuse it to the quilt before quilting or to the block before piecing, if possible, and then stitch around it with the machine. I like satin stitch and blanket stitch. When I quilt the finished top, I do not quilt the applique. I do like to quilt a few lines around it if it's big enough to feature.
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