Sandy, I did not use staples or anything else. If you wet the cardboard and then top it with soil it should stay put if you are on relatively flat ground. I had no trouble mowing because I rimmed the area with border stones. If you didn't do that, I would think your mower would still be okay around the edges if you don't have it set really low. It certainly wouldn't hurt to use staples if you wanted to, however. Nan is right that you need to overlap the edges of the cardboard or paper so there are no gaps.
Nan, I totally agree that your idea of putting out potted plants to decide on your landscape design is great. I started redoing the area in the back of my house and have been moving all the pots around until I have the look that I want. And that's a beautiful garden, by the way!