There are many tutorials on the internet that show how to insert a zip but not on the critical last stages of finishing it off. Here are instructions on how to attach the lining and finish the zip professionally with no bulky bits of fabric.
Purple Fabric: Right side
Green Fabric: Lining
Insert your zip. (This works best with an invisible zip)
There are lots of tutorials on the net and Burdastyle on how to do this.
Ensure your zip ends are even and the two sides of the fabric are perfectly even at the top.
Turn under 1cm of the lining on both sides and press.
Place right side of lining onto the right side of the dress fabric.
Put it 1/2cm - 1cm from the centre of the zip.
Pin then baste (orange stitches).
When you pin and baste the lining to the outer fabric make sure you don't catch the zip and the fabric to the far side of the zip. Leave that free
For both sides, fold the outer fabric along the stitch line towards the inside.
Pin and press
Undo your zipper then place the top edges of your fabric even with each other.
Feel with your finger where the end "nub" of the zipper is and mark with ruler and chalk across both sides so your stitching line matches up.
The line is about 1 - 2mm above the nub.
Join the outer to the inner by sewing across the top of both sides.
The stitch line is even with the chalk mark.
Trim about 1cm from the stitch line.
Cut across the corners slightly but not too close to the stitching.
Turn the fabric back to the correct side making sure the corners are nice and square.
Press the top edge flat and pin the lining to the zip.
Hand stitch the lining to the zip using your favorite invisible stitch.
Make sure the stitches do not show on the outer dress fabric.
Press your zip on both sides of the garment and sit and admire your perfect zip.
Do an approximate fit of your garment and then place your zip in.
If you are doing a centre back zip do final fitting at the sides.
If you are doing a side zip do the final fitting at the back.