How is magnetism ''conducted'' through a non-magnetic metal? I have a ball of metal about an inch in diameter and a concave disc of another metal (which is magnetic) around the ring of the disc (about $12 {\rm mm}$ in diameter). I don't know which metals they are. The ball is not magnetic on its own. That is paramagnetism, right?
The magnetic ring is strongly attracted to the surface of the ball, 'sticking' to it. However, I can stick a paperclip on the opposite side of the ball as if it has become magnetic itself, until I remove the magnetic ring from the ball.
When I wave the paperclip the same distance from only the ring itself, I feel no force at that distance.
Has the strong magnetic field of the ring caused a temporary magnetic alignment through the metal of the ball, allowing the paperclip to be attracted to it while the ring remains?
 A: The phenomenon you describe is ferromagnetism not paramagnetism. 
Ferromagnetic materials like iron behave as if they contain many tiny bar magnets (called magnetic domains if you're interested to pursue this further), but because the magnet domains are aligned randomly the fields cancel out and there is no net magnetic field. 
However if you put a ferromagnetic material in a magnetic field the external field will cause partial alignment of the magnetic domains. This induces a magnetic field in the originally unmagnetised iron, and that's why your paper clip sticks to the ball. However if you remove the external magnetic field the domains will go back to their original alignment, the net magnetic field will go back to zero and the paper clip will fall off again.
If you apply a very strong field and/or combine it with heating and cooling you can permanently change the alignment of the magnetic domains so they remain aligned when the external field is removed. This is how you make permanent magnets.
