Floorshow Garter Belts

My best guess is the metallic red ribbon is attached with a zig-zag stitch to some elastic while it's being stretched.  This will make the entire garter strap curl up on itself, but you might be able to flatten it with an iron. Definitely test your ribbon/method with some scrap pieces first. 

Columbia's photo shows that the middle/side strap is attached on top of the garter belt (the other straps are likely sewn into the designated seam).

Rocky's garter belt gives some insight on the fabric - definitely stretchy (not a plain satin).