This is an iris mechanism built into a greeting card sized card. This version also has slots on the back that allow you to place a 2"x3" photo behind the iris to reveal a picture when the mechanism is operated.
The design files can be downloaded here: http://www.thingiverse.com/thing:8788
The paper needs to be fairly thick because it needs some stiffness to operate. I use a 14 point (0.014") paper
It can be cut by hand, but it would of course be much easier on a laser or paper cutting machine.