This is a great tutorial on how to insert an invisible zip.
Actually, the whole By Hand London blog is great. Do check it out.
Do make sure you use a zip that's at least 4-5cm (around two inches) longer than the opening you want. The lower end will dangle on the inside of your skirt but this is much preferable to messing around with pulling the zip pull up while you're in the middle of stitching along the sides. With a dangly end you can stitch each side all the way down in one go. It makes sense once you try this!
Leave the back centre seam unsewn (if you are going to insert the zip into the back centre seam of course).
You need an invisible zip sewing machine foot. Inserting an invisible zip without this is the proverbial pain in the backside. Once you own one you'll be forever grateful that someone had the good sense to invent them.
Try pressing the zipper teeth aside (as per this tutorial), I am told it makes stitching easier and more accurate.
This tutorial also shows very clearly where you need to start closing the back centre seam once the zip is in. Lots of tutorials don't show this, which is why I was never that clear about what you're supposed to do at this point.
The description says to start the back seam about a half centimetre away from where you stitched before. That's half a centimetre horizontally away from the stitching line, not vertically as I first thought. The photo thankfully clears up that potential confusion.
If back-stitching isn't suited to your fabric because it makes the end of the stitching line too bulky: reduce your stitch length to the minimum your machine will give you (around 1mm or otherwise 1.1mm) and use this for up to half an inch, then increase the stitch length back to normal. The resulting tiny stitches will hold your thread. You can take the thread ends back below the end of the stitching line and back stitch them by hand a couple of times in a suitable place. If this will show through you can try to whipstitch the ends around your stitching line (on the inside)