Silk ravels like crazy, so you'll need to do something with the edges WHEN you start cutting out your quilt pieces - either use a 3 thread overlock stitch on a serger or pinking shears. Sometimes, pinking shears are NOT enough with silk. You'll have to experiment. If it's light weight, stabilize with a very light weight fusible. Personally, I think fusible is easiest, because silk ravels when you just LOOK at it!
If it's not already raveling like crazy, it's probably NOT silk. LOL But it DOES look like it's raveling in the picture.