Lesson 1: Basics
For most Housing tricks you need two small carpets. They don't have to be this kind, tatami floor mats work as well.
This trick is the one I use constantly. It's used to move objects where they normally wouldn't fit. Just move the required items like this. Connect the two small carpets so they are just barely touching. Then put the item you want to move (in this case, a rock).
Click on the carpet closest to the rock, and move it to where you want the rock to be.
Removal is just as simple. Just pick up the carpet farthest from the rock.