This is a good, basic tutorial for putting in an invisible zipper:
(Note how important it is to close your zipper after sewing up one side to mark where the bodice seam is. That will make life so much easier when you are ready to sew the other side of the zipper in place and need to match up your seams.)
Isn't that the prettiest thing?
One additional thing I always do when sewing in a zipper is to adhere it with fusible tape like Steam-a-Seam. Just for extra insurance against movement.
The other thing I do is hand stitch that last inch or so above the bottom of the zipper because I can never get close enough to the teeth with my zipper foot...trying to work around that pull is near impossible to me, so I came up with an easier solution, which guarantees a neat result.