You can go the simple iron filings on a white piece of paper route if you want to see the invisible fields surrounding a magnet. But I prefer this DIY contraption which carves 3D foam sculptures of them instead.
Using a simple electric motor with a drill bit attached that works like a CNC machine, the fairly rudimentary carver is guided by an analogue magnetic sensor detecting the strong field around a rare Earth magnet. As the rig moves back and forth making its cuts, a simple microcontroller ensures that whenever a magnetic field is detected, the drill bit is pulled back. So over time you're left with a 3D sculpture that roughly represents the fields surrounding the magnet. [Make via BoingBoing]