Remove the insulation from the last couple of cm of the magnet wire, at both ends, with the sandpaper.
Wrap the magnet wire around and around the pen, to make a coil. Leave 4cm at each end free. Remove from the pen and twist the ends together a few times to secure the coil. The uncoated ends should not be touching.
Tape the coil to the bottom of the cup, with the coil lying flat.
With the headphones removed from the headphone jack, strip the insulation off to reveal the bare wires underneath. Twist any strands of wire together to hold them together. Twist each headphone wire around each of the magnet wire ends, then wrap each in foil to make a good connection.
Start the music on the music player, plug in the headphone jack and turn up the volume.
Hold the cup against your ear with one hand, and hold the magnet against the coil with the other.
You should hear the music, maybe quite quietly. A stronger magnet, or multiple magnets, will make it louder.
The electrical signal through the coil from the music player, turns the coil into an electromagnet. The magnetic field changes with the changing electric signal of the music.
When the magnet is placed against the coil, it alternately attracts and repels the changing electromagnet's field, so pushing then pulling the coil away from it. This pushes the bottom of the cup in and out, which in turn, pushes the air near it back and forth. This is a sound wave is magnified by the cup, so that we can hear it.