I marked my skirt with pins the sections I thought needed to be widened. Using tailor's chalk, I transferred the marks about 3/8 of an inch from the side seam (I wanted 1.5 inches total let out of the widest part of the hips). With my French curve, I sketched a new side seam on the inside of both sides of the skirt and lining and gently tapered towards the waist and hem.
I sewed the new seams along the chalk line (both sides of skirt and lining). Merging the new stitches with the old at the tapered points, I backstitched a few times to lock the stitches in place.
I cut open the old stitching and pressed the new side seams with a hot iron. After that, I hand washed the skirt to remove the fabric creases and old stitch holes.
And that's all there was to it! Please excuse the wrinkles; the skirt is cotton and I was wearing it for quite a while before photographing.