Note: Insert the invisible zipper before sewing up the rest of your seam.
Step 1: Take a moment to look at your invisible zipper. You'll notice that the teeth are actually folded over the zipper tape. With your finger, you can gently unfold it (as in the picture). As you sew the zipper to your garment, you'll want to unfold it so that the needle of your sewing machine gets as close the to the teeth as possible. A special invisible zipper foot will help keep the teeth unfolded, but a regular zipper foot can work if you're careful. When the seam is sewn and the zipper teeth are folded back into place, the seam will actually lie beneath the zipper teeth, making the zipper invisible from the front of the garment. Cool, right?!
Step 2: With the zipper unzipped, pin or baste one side of the zipper along the raw edge of the zipper opening, right sides together so that the zipper is facing down and the teeth inward. Sew from the top of the garment down, with the zipper foot as close to the teeth as possible. Make sure to keep the teeth unfolded if you don't have an invisible zipper foot to help you. Stop sewing and secure your stitches about an inch before the end of the zipper tape.
Step 3: Line up the other side of the zipper with the other side of the zipper opening, right sides together. Make sure that the zipper and fabric are even with the other side, and that the zipper is not twisted. Pin or baste in place.
Step 4: Sew the zipper to the zipper opening as in Step 2.
Step 5: To close up the rest of the seam, zip the zipper closed and place the fabric right sides together. Still using the zipper foot, place the machine needle about 1/8" away from the zipper tape, 2" above the bottom of the zipper. Sew past the end of the zipper and continue down the rest of the seam, making sure not to catch the zipper in the seam.
Step 6: Inspect your new pretty (invisible) zipper! If there are any areas where the zipper tape shows through on the front of the garment, you can leave your original stitches in but sew a second line of stitching even closer to the zipper teeth.