How does salt melt ice?
To put it plainly, salt lowers the melting and freezing point of water. Pure water freezes at thirty-two degrees Fahrenheit. At that temperature we can say that the rate of freezing is the same as the rate of melting.
In other words, at water's freezing point there's a sort of equilibrium between freezing and melting. Throwing salt on ice upsets the balance.
The salt dissolves into the liquid water, which means that some of the water molecules are replaced by salt. Since there are now fewer liquid water molecules to be captured and frozen by the ice, the rate of freezing drops.
Since the rate of melting stays the same, there's more melting going on than freezing. And so the ice melts. Anything that dissolves in water will do the trick. You could pour sugar on ice and it will melt. But I guess since salt is cheaper it's used more often.