This is the most simple way to sew the Fold-over-elastic over a fabric edge:
Fold the elastic in half along the center crease, and align it under your presser foot so that the inner edge of the foot lines up with the edge of the folded elastic.
With the needle down, lift the presser foot and slide the fabric inside the fold of the elastic, positioning it as close as possible to the crease. Lower the presser foot, gently stretch the elastic to the desired length, and begin sewing. Line the edge of the inner edge of the presser foot to the edge of the elastic.
As you stitch, make sure the fabric stays securely inside the fold, and maintain even stretching for a smooth, professional finish.
One side of the fold-over elastic is shinier than the other side. This is usually used on the outside (Some people prefer the matte side).There are two things that this elastic does in one go – it serves as elastic and also as a binding tape—the elastic stretches to its double-length..

A zig zag stitch is used to sew this elastic tape because this is a stretchy stitch. A straight stitch will break when stretched.
Stitch setting: Use a narrow regular zigzag (length: 2.5–3.0, width: 2.0–3.0) or a 3-step zig zag stitch.
Adjust your stitch type to zig-zag and stitch width to 2 or 3 if you want a narrow zig-zag, use 2. And a stitch length of 2. Fold the elastic tape over the fabric edge
Method 1 – Sewing over the edge of a stretchy fabric.

Sew from the top, catching the top fold of the tape, fabric edge in between, and the bottom fold of the tape.

Ensure that you are stitching through all these layers at all times.
Pro tip : If Fold Over Elastic (FOE) drives you nuts when stitching it with a regular sewing machine, try using a coverstitch machine instead.
Why? With a regular machine, you may make two stitching—first to tack the fabric in, then to finish the fold. That adds a lot of thread into the elastic, which can stretch it out permanently. Once FOE is overstretched, there’s no fixing it.
A coverstitch gives you a clean, stretchy finish in one pass, without overloading the elastic—and your nerves.
Method 2 – Sewing the fold over elastic over the edge of a non-stretchy fabric or for gathering
Take fabric double the length of the fabric. The fabric automatically gathers to match the stretch of the elastic.
You should stretch the elastic as you sew, that is the trick- this will automatically gather the fullness of the fabric to match the elastic stretch.

Here is a video explaining the process.
Pro tip : When sewing the fold over elastic, if you have a problem slipping or the machine not moving forward, use a walking foot
Fold-over elastic is a particular type of elastic tape that is used as a binding elastic in sewing – it has enough width to go over an edge and a dent down the center of the elastic on either sides, which aids in easy folding over fabric edges. I find this unique type of elastic extremely useful in many of my projects.

Uses of Fold over elastic.
Other than for sewing on waistbands, Printed fold-over elastic is perfect for neckline accents, headbands, flat trim, or hair ties. Here are the most common uses for this versatile elastic.
Finish garment edges
FOE is often used to finish the edges of garments, such as necklines, sleeves, and leg openings in lingerie, swimwear, and athletic wear. It can be used along waistline and sleeve hem edges of blouson tops. It provides a clean, stretchy finish that’s comfortable against the skin.
Other than folding, you can use it as it is on top of the fabric as well – it is soft and smooth enough to be on the surface of the fabric. This is usually used on the waistline edge of underwear.
Used in baby clothing
Fold over elastic is soft and stretchy. It is perfect for use in diaper covers, baby hats.
Used to make hair accessories
FOE can be used to make hair accessories like ties and headbands. Its soft texture and stretchability make it gentle on hair, reducing the risk of hair breaking.
Binding and Piping
FOE can serve as an alternative to traditional binding or piping in projects like blankets, quilts, and more, giving them a unique and colorful edge. It is usually used to bind the leg line edges of panties
Straps for clothes
FOE is used for making straps for slips or camisoles. You can also use it in one go to bind the neckline and then go over as the strap.
Make Stretchy bracelets
You can sew stretchy bracelets using fold over elastic quite easily.
Related post : Which elastic to use in sewing ; Different types of sewing tools.