I start by making a square card that is slightly larger than the die I am using. For instance, if the die is 4 inches wide, I make my card 4.5 x 4.5 inches. You need the extra space to tape your die down, but you don't want to make it too big, or you're just wasting cardstock.
The next step is position the die on the fold in such a way so as it doesn't cut all the way through the fold (see above). I try to get it as close as I possibly can, to preserve the shape, but yet keep enough so that the card will open and close nicely. This took a few practice tries to get it just right, so use some scrap cardstock on your first few cards.
Once I get the die where I want it, I tape it down with Scotch tape. I usually stick the tape to the back of my hand a few times so that it's not super sticky and hard to remove later. You want to make sure that you don't place the tape on the inside of the die, which will become your card. You want to stick it to the "waste" part of your cardstock, outside of the die. Are you still with me?
Now run it through your die cutting machine! I have a Cuttlebug and it works just great! You will need to run it through two or three times, depending on the thickness of your cardstock. You want to make sure you get a nice, clean cut all the way through. When it's cut, you simply remove the tape and the die, and you have a hinged card in a unique shape! And here's what I did with mine:
Please feel free to contact me if you have questions. This is much easier to do when you're "hands on" rather than just reading it. Give it a try!
Stamps: Heart Prints (PTI)
Ink: Dark Chocolate and Raspberry Fizz (PTI)
Cardstock: SS White and Raspberry Fizz (PTI)
Ribbon: Brown satin wired
Tools: Medium Heart punch (EK Success), Tiny Tags for Cuttlebug (ProvoCraft), Labels One Nestabilities die (Spellbinders), Cuttlebug (ProvoCraft)
Other: foam mounting tape (3m)