Facings and understitching are quite easy when you get the hang of them. They just take a little care, as they are usually on curved openings like neck and arm holes.
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Facings go on the inside and stop these openings fraying and getting in a mess. They follow the shape of the garment, so help it to keep its shape too. Even though they should not be seen from the outside, they still need to be sewn and finished as carefully as the garment they are to fit. They are frequently sewn or bonded to an interfacing to help them do the job properly.
If you cut the garment pieces accurately, and also cut the facing and interfacing carefully, they will fit together and the garment will look good. The first part of this is the preparation. Make sure that you follow the grain line carefully when laying out the pattern for both the garment piece and the facings. The next thing to do is cut out carefully, making sure that the notches are cut accurately, as these will help you to line up all the bits once they are sewn together. Follow the diagrams and the instructions in your pattern carefully. The following will help you:
Identify your garment pieces and make sure you have cut them out correctly: identify the glue side of iron on (fusible) interfacings before you cut them out.
Apply your interfacing to the facing in the way dictated by the instructions. ‘Iron-On’ implies a swift swipe over with an iron, but it takes more! It takes about 20 seconds for each iron sized section to fuse properly. There is a lesson on how to do this in the Pressing Problems page. Use a pressing cloth on the board, and a damp pressing cloth between the interfacing and the iron.
Stay stitch the curved seams to be faced, about 1/8″ (2mm) inside the seam line in the seam allowance.
Assemble the garment and facing pieces in the correct order, to the point where you need to apply the facings.
Press the seam allowances open on both facings and garment pieces, on a plain seam as in the illustrations. Press seams carefully when using other seam types. Facing seams are usually done as plain seams to avoid bulk.
Clean Finish the outside edges of the facings: look at the zigzag line in the illustration. Use whichever clean finish is appropriate to the fabric and the garments you are making.
Sew the facing to the garment, matching seams and notches. Your stitching line should be just outside the stay stitching line.
Clip into the seam allowances from the raw edge towards the seam line. Be careful NOT to cut the stitches! These little snips will help the facings and the seam allowances to lie flat once the garment has been completed.
Fold the facing to the inside, and press down carefully, rolling the seam line to the inside very slightly. This helps to hide the seam line round the edges and gives a neat finish to the garment.
Fold out the facing so that you can see the right sides of both the facing and the garment. The garment will not lie flat, so be careful! Fold the seam allowances towards the facings on the under side. You may find it easier to control if you tack the facings and seam allowances together. Stitch close to the seam line on the facing side, being careful to sew through all the seam allowances. This line of stitching is called Under Stitching.
Fold the facing back to the inside of the garment and give it a last pressing. Where the facing crosses the seams, catch it down with a few stitches over the seam allowances on the inside.
The illustrations here have been shown using what we call the Flat Construction Method. The final seam (in this case it would be the side seam) is done last.
The neck could be faced using exactly the same construction techniques, or, if it was a large enough opening, it could be done in one piece by sewing up both sides of the facing and the garment at the shoulder, so that both formed rings.
Remember these illustrations show only half the garment!
Scroll down to the final picture to see how it should look from the outside.
Understitching can be used as above for arm and neck openings, and also for skirts and trousers without waistbands. Below you can see photographs of understitching a facing on a real garment.
Here you can see where the stitching goes in through the facing and, under it where you can’t see it. all the layers of seam allowance. The facing is the plain blue fabric and the lace is the outside or fashion fabric.
Do be careful to make sure that all the seam allowances are lying flat and are facing towards the garment facing before you stitch. I find it easier if I clip the seam before understitching.

Here's a close up to show you how close to the fashion fabric you need to be - very close! 1/8th of an inch or 2 mm is about right!

Completed understitching - a neat row parallel to the seam, but not touching it at any point.

When you have clipped and understitched a seam, it will lie flat, with just a tiny amount of the fashion fabric showing on the inside.

See!

And from the outside the neck of this dress lies flat without the row of stitching showing. This is one of a set of costumes for my Romeo and Juliet project.