The process they are describing is called applique. There are dozens of videos on YouTube teaching this technique as it is very popular for quilting.
Heat n' Bond, Stitch Witchery and Wonder Under are brand names of heat fusible webbing. It's great stuff, I use it constantly for lots of different types of projects.
The smaller and more delicate a fabric bit I'm cutting & appliqueing, the heavier I want my fusible webbing. Yes, it comes in different 'weights', for a task like this I would use at least Medium if not Heavy. While it sounds more complex to cut a lot of bits out of a long strip, it isn't that bad as long as you have good sharp scissors. It's very easy to mess up a project when you have un-attached pieces and are trying to line them up perfectly.
How I would do it:
- cut a strip of yellow fabric the width & length needed
- cut a strip of blue fabric twice as wide & the length needed* (you'll see why later)
- first of all, I'd do the applique in a long strip then sew this decorated hem onto the dress, makes the whole thing gobs easier.
- iron my fuseable web to the back of the strip of yellow fabric. on the paper side draw out the design
- cut out the inside D shapes first, then the outside scallops so I have one long yellow lacey bit
- carefully lay it out then iron it to my blue strip, lining it up at the top edge (lots of blue extra below the scallops)
- use a tiny zig-zag stitch to sew the two together (this is the time consuming part)
- fold your blue under and press, ensuring the yellow hits the bottom edge all the way around.
-catch both raw edges at the top when you sew the hem onto the dress.
* this is to create a folded hem instead of a rolled one. Folded hems are wonderfully easy but only suitable on items like this where the hem is a different fabric. The other advantage of a folded hem is that it guarantees you the design will go to the edge exactly, because you aren't folding it until after the design is applied.