How does electrolysis work?

Electrolysis is essentially the movement of charged ions in a solution.For example, take sodium chloride, NaCl. NaCl is the electrolyte. The electrolyte is a substance, usually a salt that when in liquid form or in solution, will dissociate into its ions (NaCl -> Na⁺ + Cl^-). When a charge is run across the electrodes, the ions will move to the electrodes with the charge that is the opposite of their own - think opposites attract so the POSITIVE sodium ions (cations) will move to the NEGATIVE electrode (anode) and gain an electron becoming UNCHARGED. The NEGATIVE chlorine ions (anions) will move to the POSITIVE electrode (cathode) and lose an electron becoming UNCHARGED as well.