The cup needs to be folded for insertion and removal, and there are many ways to do this.
The Menstrual Cup community on Live Journal has a lot of posts regarding folds http://community.livejournal.com/menstrual_cups/tag/insertion%20-%20folding%20methods
I use the “C” fold. I fold the cup in half (with both hands), and hold it in that position with my first finger and thumb – running down the length of the cup, so that my fingertips are at the rim end.
Here is a video showing Cup folds you might find useful