Charge is not generated in this manner -- as far as we can tell, electrical charge is a conserved quantity -- we have just as much now as there was at the beginning of the universe (which should be a net zero). You can create particles and antiparticles at the same time, and these have opposite charges, but varying a magnetic field does something else.
What it does is to create an electric field which can push mobile charges around and impart energy to them, which can be used for other purposes. The full specification of this is Faraday's law of induction, which, in integral form, says that the time rate of change of the magnetic flux through a surface (that is, the sum of all the field lines penetrating the surface), is related to the line integral of the electric field around the perimeter of that surface.
If you have a loop of wire, the surface you'd get if you put a soap film across the loop (for example) is a perfect situation. If you change the magnetic flux through this surface, say, by inserting a magnet and taking it out, you will cause current to flow in the wire because of the integral of the voltage around the loop of wire. Break the wire and put a light bulb in there, or something else, and you have a useful electrical generator. Substitute another loop of wire with a changing electrical current through it for the moving magnet, and you have a transformer.
The materials the magnet and coil are made out of don't matter much. They can be "lossy" in that when current flows through the coil, Ohmic resistance can reduce the usable voltage. The magnet may be less strong if it's made out of iron than if it is made of a new, high-tech cobalt-samarium alloy or other nifty magnet materials.
(published on 09/08/06)