Invisible zips in garments give a smooth appearance, because no indication is given of how the garment opens and closes. A fabric covering and the position of the zipper teeth create the illusion of the zipper being invisible. A special zipper foot is then used to lay a line of stitching close to the zipper teeth, creating what looks just like every other seam on the garment.
Begin with an open seam--no part of the seam that is getting the zipper should be sewn yet. Place the fabric face up on a flat surface.
Place the other side of the garment face up on a flat surface. Put the piece of the garment with the zipper attached face down on top of the piece without the zipper. Pin the edge of the zipper tape 1/8 inch in from the raw edge. Re-open the zipper.
Fold the fabric so the right sides are together. Sew the seam from about 1/4 inch below the end of the zipper tab to the end of the garment. Press the seam open.