|This technique comes from Threads, July 1998. The URL is for ordering this as a back issue. The article has good illustrations. Here is the basic technique:
1) Complete the entire vest, up to the point of stitching the lining to the fashion fabric. Stitch the neckline, the armholes, and the bottom edges for both the front and the back. The only open seams will be the side seams.
2) Turn the vest as such: Place it on a table (either side up) with the back pointing towards you and the front pieces facing away from you like a "Y". Reach into an open side seam on the back section, grab the corresponding front piece (one of the prongs of the "Y"), and pull it right through the same open side seam on that side of the back. This will miraculously turn the vest right side out on that side.
3) Do the same thing with the other front piece.
4) Stitch the side seams as such: match the lining and fashion fabrics, right sides together. You will stitch in a circle as far as you can around the side seam. You won't be able to complete the seam on the machine. Go as far as you can, and complete the seams with hand stitching. If you hate to hand stitch, you can machine stitch over the over the seam, the last bit of open seam will slide right into the side of the vest.
5) Machine stitching will show, but it's the side seam and won't be really visible.