How to measure the electrical conductivity of a substance?
A lot of work was done in the 19th and 20th century on determining the conductivity of aqueous solutions. It was a huge field called conductometry (check Wikipedia). You experimentally measure the resistance of a solution by placing the desired liquid between two inert electrodes and pass high frequency alternating current to prevent electrolysis. In solutions, electrical current is carried by ions. If your solution has ions or if it is ionizable, it will conduct electricity. Now you can determine which solution has ions based on ionization, e.g. you can write $\ce{HCl (aq) -&gt; H+ + Cl-}$ and can predict that it must be a conductive solution. In fact, the aqueous $\ce{H+}$ has the highest conductivity known in water. $\ce{OH-}$ is next.