I'm sure there is a correct name for these things, but I haven't come across it, so I'm calling them Chain Puffs. This is a really nice trim, it's easy and takes a lot less fabric than ruffles or ruching. It was very common on gowns and petticoats in the 18th century.
It can be cut on the straight or the bias, but I think straight is easier.
Step 1: Cut or rip fabric strips. These can be self-fabric or a contrasting fabric. Lightweight fabric (silk, taffeta, cotton, etc.) works well and 3" is a good width to start with. You can use heavier fabrics, but plan on covering the ends with something else... like a rosette!
Step 2: Sew all strips together (see comment on Ruching post)
Step 3: Sew strips into a tube and turn. DO NOT press. Leave it puffy. If you use sheer fabric, you can stuff the tube with a smaller tube at this point.
Step 4: measure & mark the intervals you want the puffs to be. I marked every 2" on this garment and it looks great. You could do shorter with lighter fabric, or longer if you used a wider tube.
Step 5: Gather the fabric into a W shape by pinching up the center then pulling up the edges at your marks. Make a small stitch in the center or at the bottom. Do not overcast onto the top side, you don't want your stitches to show. Tie your thread off and repeat until you've pinched the length of the tube. At this point your puffs will be a bit sloppy, don't panic you'll finish them later. Bury the ends of your threads or cut them very short.
Step 6: Arrange the chain on your garment and pin each puff. Don't stretch them sideways too far or they will pull on the fabric. Make sure there is a little give length-wise so there is room for more "puff".
Step 7: Cut a comfortable length of hand-stitching thread and stitch the ends under the first puff or plan on covering the raw edge.
Tack each side down and then tighten the pinch with several passes through the center near the top of the pinch. Tack the pinch to the garment.
Try to keep your stitches small, and make sure you don't pull too tight. Keep the threads between the fabric & lining, or inside the puffs so it doesn't show. Keep your stitches small and hidden. The blue line shows the easiest thread path.
Step 8: Tuck the raw end under the last puff or cover it with another bit of trim.
Here's a close-up of the finished chain puffs.
Sorry it's dark, I'm on my husband's computer and he doesn't have an image-editing program.
This chain was made with a heavy cotton, and is very heavy. It's the look I wanted, but I won't be using something that thick again. You could actually iron these things and they wouldn't flatten much.
Use lightweight fabric if you decide to do this.