You can make a beautiful, embossed edge for your cards using your Nestabilities. The extra long rectangles work best for the long edge of a card but if you want to put an edge on a mat or other card element you can use a smaller Nestie.
Position your die on your card with the lower edge under the raised cutting edge and the top of the card (fold) on top of the flat side of the die. This way you will only cut on one edge. Tape in place with removable tape so it doesn't shift when you cut it out. Put into your die cutting machine as usual.
You can also emboss your card edge (using the tan embossing mat) to give it a nice finish. You'll notice that you get an impression of the other edge of the die on the top of your card. There are a couple of things you can do with this. One, cover it up with another layer of cardstock or patterned paper or two, use it in your card design.
Here's my finished card. I chose to cover up the impression on top for this card.
Supplies: Cardstock (Papertrey Ink - kraft, white; Stampin' Up), Patterned Paper (My Mind's Eye), Stamps (Cornish Heritage Farms - mice; Whipper Snapper - sentiment), ink (Adirondak, Ranger), Copic markers, ribbon (Stampin' Up!), jingle bell, die cuts (Nestabilities)