Great question, but the answer can get complicated. For those metals which are well described by free-electron theory, however, you might track down information using two key search phrases: "Drude model" and "Hall effect".
The key idea is this. In a magnetic field at right angles to the electric field, electron paths curve due to magnetic forces before they hit anything and scatter. The result is some sideways current or voltage, depending on whether the circuit lets that sideways current flow. That's called the Hall effect. If you have a few electrons with long free paths between scattering, the curvature is important and you get a big Hall effect. If you have the same conductivity but from many electrons with shorter free paths, the Hall effect is reduced.
If the current is carried by 'holes' (missing electrons) it acts like the carriers are positively charged, and the Hall effect has the opposite sign. If there are both electrons and holes, it gets much messier.
So the basic technique is something like this:
Take a thin foil (or evaporated film) of the metal in question. Cut it into a sort of cross shape. Run current one way through the cross. Measure the voltage at right angles in the cross. Now apply a measured magnetic field pointing into the plane of the metal. An extra voltage will appear on the right-angle part of the cross. That's the Hall voltage.
You can calculate the effective concentration of electrons or holes from that, using the more detailed sources I'm sure you can find with the search terms I mentioned.
Good luck on a nice project.
(published on 12/25/2009)