One of the most unique aspects of an invisible zipper application, is that the zipper is fully stitched to the seam edges first, after which the rest of the seam is completed at the bottom. During the application process, the zipper is kept fully open and each zipper portion is aligned and stitched individually to each corresponding seam edges. That being said, it is important that each zipper portion is aligned evenly along both edges- you can use the seam's top horizontal edge as a guide.
Once the invisible zipper is fully stitched, the bottom should be open while the closed zipper should resemble a regular seamline at the top.
To complete the seam housing the invisible zipper, align the bottom seam edges you would any regular seam: face sides touching and edges aligning. Move the bottom of the zipper tape away form the seam allowance to keep it as flat as possible, and insert pins perpendicularly through both seam edge as shown.
Using a zipper foot, align the machine needle as close as you can to the bottom of the existing zipper application stitch. Machine stitch the bottom of the seam at the designated seam allowance (1/2" in the image above). Once you've stitch for about 3-4 inches away form the zipper, you can switch to a regular zipper foot and stitch the remainder of the seam in a conventional fashion.