To test the conductivity of different metals, you will need:

1. Samples of each of the metals you want to test. Make sure all the samples have the same dimensions (cross-sectional area and length). The easiest way to do this is to get wires of the same gauge (diameter) made out of each of the materials that you want to test, and cut them to the same length.

2. A digital multimeter. This is an important and handy tool for many electrical tasks.

3. A ruler.

Now that you have all of the materials:
1. use the multimeter to measure the resistance from one end of the wire to the other. Do this by attaching the one end of the wire to one of the leads of the multimeter, and the other end of the wire to the other lead on the multimeter. Then, with the multimeter in the resistance measuring mode, it should displace the resistance of the wire (measured in ohms denoted by the symbol ?).

2. Use the ruler to measure the length of the wire (use SI units such as centimeters (cm) and convert to meters (m) by dividing by 100).

Now, the conductivity of the metal (per unit length) is given by 1/(resistance*length) which is in units of 1/( ?*m) which is the same as S/m where S is the SI unit of conductivity called Siemens.

Wikipedia has a nice table of conductivity of several metals. Here is the data for some of the metals you mentioned so that you can check you results and calculate the percent error for you experiment [%error=100%* (actual value- experimental value)/actual value]

Copper 5.96×10⁷ S/m
Aluminium 3.5×10⁷ S/m

The conductivity of metals is related to the charge carrier density (such as how many electrons are free to move about the metal and flow in response to an electric field) as well as the charge carrier mobility (how freely the charge carriers can flow through the metal). Different metals have different charge carrier densities as well as different charge carrier mobilities which results in different conductivities. Many factors affect the charge carrier density and mobility including things such as the chemistry of the material (such as what atoms are in the materials and at what ratio) as well as the structure of the material (crystalline, different crystal structures, as well as other ordered or disordered structures).

Many fields work with metals and their electric properties. One such field is Materials Science. I am a graduate student in the materials department, but there are many areas of material science, and not all of them work with metals.